The Players May Not Want To
Part of fantasy role playing for a lot of people is being able to be larger than life for a bit. They may not want their characters to feel fear at all.
Now, in a novel this may be a bad thing, since a character that isn't believable can disrupt the suspension of disbelief. But in an RPG its not necessarily a bad thing to let the players through their characters simply feel fearless and powerful, even in the face of overwhelming odds (which in your example weren't horribly overwhelming since they won.).
Their reactions might not be quite that unbelievable after all
People can keep their fear under control. When I was in the Army, I was in an Airborne unit and we did jump training frequently. I was scared every time. I still jumped out of the plane, every time. I was lucky enough that I never got in a close quarters fire fight, but plenty of people in my unit did. Not a single one ran in the time I was with that unit. Many of them did readily admit they were scared. They didn't run and the few times I heard about screaming involved people with serious injuries.
Remember, we aren't talking about some comfortable bookkeep that has never even been in a fist fight. Even a first level adventurer has mentally prepared for battle, equiped themselves for battle, and trained for battle. By the time they have added a few levels they have seen the horrors of battle and possibly the terrors of war. They know how to stand their ground.
Sure, a good role-player, when their character faces a new, powerful threat, might add details like, "My eyes widen in terror, and I feel my heart pounding in my chest." But, especially if they have a good reason to stand their ground (like a young child they must protect...), its not actually that unrealistic for them to follow with, "But I swallow my fear, and yank my sword out of its scabard!"
Remember that 300 was dramatized and fictionalized, but it was based on a real event. 300 Spartans (backed up by 700 Thespians and 400 Thebans in real history, so about 1400) stood their ground against genuinely overwhelming odds. The Persian Army was somehwere in the neighborhood of 300,000. With odds of nearly 300 to one, the Spartans knew that they were waiting for death (indeed very nearly all of them were killed). I suspect close to all of them were terrified, most of them were young men with little experience. They stood their ground.
Unfortunately there's nothing within the rules that dictates how a Druid must act. Though, the introduction to the class clearly states
Druids are also concerned with the delicate ecological balance that sustains plant and animal life, and the need for civilized folk to live in harmony with nature, not in opposition to it. (PHB, pg.65)
Druids are also part of larger organisations, called Circles, the description of which includes this line:
Druids recognise each other as brothers and sisters. Like creatures of the wilderness, however, druids sometimes compete with or even prey on one another. (PHB, pg. 68. Emphasis mine)
There's no information on how to punish a druid for living in disharmony with his or her environment, but it seems clear that they believe in the natural order; the laws of nature. Even when it means the strong hunt and prey on the weak. A druid is certainly not forbidden to kill animals, especially if it's for their own survival. Hunting and preying is the natural way.
And they are certainly under no obligation to constantly care for all plants around them. But perhaps going out of their way to destroy them would cross the line, though.
A Character's behaviour is not governed by their class
One thing to keep in mind that a character's class is a mechanical term and used within the game to determine their capabilities. Within the world, their vocation may be quite different. Perhaps the Bard is simply a charismatic politician, swaying the populace with powerful speeches instead of moving song. Perhaps the Wizard is actually a hedge mage, carefully tending his garden in solitude and communing with natural spirits instead of actively researching in a library, locked in a tower.
Acting stealthy, picking locks, and thievery aren't specific to a Rogue. Rogues simply specialize in such tasks. Plenty of warriors enter a battle rage, Barbarians have simply learned how to channel that rage to make themselves stronger during battle.
Decide what it takes to be a Druid within your setting, and discuss this with the player
Unfortunately, it seems you've allowed the player to assume the character class without fully discussing your setting and/or their backstory, and hence their role within your world. How did they gain their powers? Are they part of a Druidic order (By the book, they are in a Circle)? Are there repercussions from this order when a Druid acts out of interest?
Maybe the character isn't a druid at all?
One thing I should make explicit is the option that perhaps the character isn't a druid in your setting at all. After you discuss Druidism within your setting with the player, discuss other flavour-based options that allow him to keep the class but still take his character in another direction. From an example in the comments maybe the PC is from a barbarian tribe that uses nature-based magic (but to survive in nature rather than protect it). There are many explanations, as many as you can imagine, as to why your Player's character would have these powers without actually being a druid within the setting; mechanically a Druid, but not referred to as such by the other characters who inhabit your world.
There are some options available if you decide he's a druid in both name and function
After you discuss with the player how druids work in your setting, explain to them why, if his behaviour continues as it is, he will face certain consequences. Importantly, though, don't punish the player for his current "misdeeds," especially if you haven't already spoken. If, after you've had a discussion, the player continues behaviour disruptive to the natural world, make a story out of it.
Perhaps their Cirlce becomes determined to hunt him. Either to bring him to justice and remove his powers, or to hunt and kill him like one would a mad animal.
Maybe the god(s) or spirits of the natural world disapprove of their actions and deem them unworthy of their druidity and remove their powers until they repents. I certainly know certain Fey may have a problem with their behaviour.
Maybe their magics start to go wrong, and the animals and plants he calls to his aid turn on him instead of acting as allies?
Perhaps an investigation by the local guardsmen has led them to believe the PC is responsible for a recent robbery?
By the book, you can take inspiration from other rules on how to act
My one suggestion would be to treat it as a Paladin who has broken his oath. A short blurb on this may be found on pg.86 of the PHB, and there is an Oathbreaker Paladin in the DMG. Suggest the character play a fallen druid (if they can exist in your setting) and find/create an such a class with them if they find this method interesting.
In the end, it is your Player's Character
Perhaps suggest the player take class levels in either Barbarian or Rogue, as they may better fit their current playstyle, but do not force them to do so. There's nothing in the rules dictating their behaviour, and it seems to me they were not aware of your expectations.
But do take the opportunity to inspire yourself and your campaign and present challenges for the player and their party. All actions have consequences.
Best Answer
Spells only do what they say they do, and although the DM's free to play up the practicalities of weird long-term spell effects, unless the description of the spell cloud of knives says it can hurt you in the ways you describe, it should't be able to. There's no mention of a cloud of knives stabbing the caster if he trips, stabbing the caster's friends while they play cards, stabbing the caster's girlfriend while they're intimate, stabbing the caster's food while he's eating, or anything. That just doesn't happen. It's magic, but it's a codified, consistent, reliable, almost scientific magic with a set range of effects and results. The DM can still mess with you, but that's house rules territory, and he should be crystal clear about what those house rules are, not force you to figure out how to make it go. (Unless, of course, your character really is the first cleric who has ever had this idea in that campaign universe's history.)
If you're allowed to fluff the spell in such a way, have all the daggers point down, hover by your knee, follow you by floating flat parallel to your shoes, or whatever to emphasize they're out of your way. It's D&D, after all--everyone's armed anyway, so what difference does it make if you're armed with a greatsword or a cloud of knives?
As an aside, being constantly surrounded by blades from a D&D 3.5 standpoint isn't that big of a deal because there's already a precedent for a similar effect with ioun stones (DMG 260-1). The stones don't--according to the description--prevent folks from sleeping (although stones can be more easily stolen when the bearer sleeps), acquiring nourishment, or interacting with others.
But there's really nothing you can do to if the DM is determined to punish you for the persistent cloud of knives, but having things circling a PC's head and being rewarded for it instead has been present since 1st edition Dungeons & Dragons.