You cannot use attack powers from other classes while in beast form.
From PHB2, p84 (as updated by official errata):
Wild Shape
... While you are in beast form, you can’t use weapon or implement attack powers that lack the beast form keyword, although you can sustain such powers. ...
No paladin powers (or powers from any other non-druid class, for that matter) have the beast form keyword, therefore they can't be used while you're in beast form.
...unless...
The exception is if you take the Werebear, Wererat, or Werewolf themes (all from Dragon 410). They all get an encounter version of the wild shape power, and at level 10 that power changes so that it allows the use of powers both with and without the beast form keyword.
Werewolf Level 10 Feature (10th level): When you use the wolf shape power, you can assume the form of a humanoid-wolf hybrid, instead of a wolf. While in hybrid form, your equipment does not become part of your new form, and you are not forced to drop any items you are holding. You are also not limited to using implement and weapon attack powers that have the beast form keyword.
...or...
If you are a half-elf and have chosen an implement power for your Dilettante racial trait, you can take the Wild Dilettante feat (from Dragon 385 and updated by official errata). However, this only affects the Dilettante power and would not apply to other powers you happen to have.
Wild Dilettante
Prerequisite: Half-elf, druid, you must have chosen an implement power for your Dilettante racial trait
Benefit: You can choose to treat the power you selected for your Dilettante racial trait as though it has the beast form keyword.
The spell is still affecting the druid, and wild-shaping does not end effects on the wild-shaper, therefore the druid is still under the effects of the enlarge spell while wild-shaped.
At this point you might conclude that the question is settled: they would be an extra-large bear, because the spell is still working that that's what enlarge does. But that's not quite right.
Let us look at precisely what the enlarge spell's effect is, not what we might be tempted to mentally simplify it as (with all emphasis mine):
You cause a creature or an object you can see within range to grow larger or smaller for the duration.
Okay, so it doesn't make it 2× in every dimension as a static fact, it makes it grow at the beginning of the spell. That would mean it would not make any further changes afterwards, only sustain the initial change.
Well, maybe I'm reading too much into "to grow". Let's see what else it says it does:
The target's size doubles in all dimensions, and its weight is multiplied by eight. This growth increases its size by one category — from Medium to Large, for example. If there isn't enough room for the target to double its size, the creature or object attains the maximum possible size in the space available. Until the spell ends, the target also has advantage on Strength checks and Strength saving throws. The target's weapons also grow to match its new size. While these weapons are enlarged, the target's attacks with them deal 1d4 extra damage.
So it does look like it's a one-time growth, based on the verbs and nouns used. In particular, if enlarge is used on a target inside a smaller space than the maximum possible size, and then the target moves out of that space, they don't grow further once there is more room — the growth at the beginning of the spell is all you get, nothing more later.
So, the conclusion there is that the druid can shapechange into a form, and the enlarge effect is not applied to the new form. If they change into a sparrow or a bear, they get the normal statistics of a normal sparrow or normal bear.
That means that a druid that wants to dodge an inconvenient enlarge or reduce can easily do so by wild-shaping, but a druid that wants to benefit from enlarge or reduce in their wild-shaped form will have to somehow arrange for the spell to be cast after they wild-shape, so that it will grow their new form instead of just their previous form.
Best Answer
Yes, you just have +5 vs reflex.
Unless you took an expertise feat (such as Totem ExpertiseDDI) to gain a feat bonus to attack rolls, then the only bonus you're likely to have at level 1 is your wisdom bonus.
The modifier for those attacks is calculated as follows:
Note that all druid beast form powers have the implement keyword, and that (as Joshua Aslan Smith pointed out in his answer) you retain the use of implements you were wielding when you entered beast form. This means you gain your implement's enhancement bonus to attack rolls. Also, implement attacks never get a proficiency bonus, so proficiency with claws is a non-issue.
At first level +5 is a perfectly good attack bonus; most enemies are going to have a reflex of 12 or less, so you'll be hitting on a roll of 7+ on a d20.