[RPG] How does a poisoned arrow combine with the spell Conjure Barrage

Sorry, No.

Jeremy Crawford ruled about the use of nets as illegal for the conjure barrage spell. So, not allowed under the Rules as the Designers intended for a character to be allowed to do so.

Conjure volley is meant to work with ammunition or a weapon that deals damage.

Damage Type

This follows logically with the text of the spell in regards to the type of damage dealt. Nets don't deal damage, so they have no damage type, and the spell clearly reads:

The damage type is the same as that of the weapon or ammunition used as a component.

And, before you ask, Jeremy Crawford already ruled, all damage has a type:

All damage has a type. #DnD

So there could be no damage done, as there would be no source of the extra damage.

No Restraint

The spell also says that the copies don't remain.

cone of identical weapons that shoot forward and then disappear

So, even if it worked, the second it hit the whole point of using nets would be lost, as they would immediately vanish.

Conjure Barrage is not a ranged weapon attack.

This does not work because "ranged weapon attack" in D&D 5e is a term of art--it refers to a specific piece of the rules, and not necessarily the underlying fiction. While the effect of conjure barrage may intuitively seem like a ranged weapon attack, it is not a "ranged weapon attack" as far as the rules are considered.

A "ranged weapon attack" is partially defined on PHB 194:

When you make an attack, your attack roll determines whether the attack hits or misses. To make an attack roll, roll a d20 and add the appropriate modifiers.

On the other hand, conjure barrage asks for a saving throw—it is the target that rolls the dice in that situation. Because it calls for a saving throw, and you don't make the attack, it doesn't work.

Compare this situation to a spell like fire bolt, which asks you to make a ranged spell attack. In this case, you're making an attack, so you roll the d20, but it's still not a "ranged weapon attack" because it's a "ranged spell attack".

Essentially, you need to fulfill all three words of the phrase. You must make an attack (you roll the attack roll), at range, using a weapon.

Note that you can't cast those spells in one turn.

The wording in your question is a bit ambiguous, but it's important to note that you can't cast both of those spells in one turn, because that would require a bonus action spell and a 3rd level spell. PHB 202 states, (emphasis added)

A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven’t already taken a bonus action this turn. You can’t cast another spell during the same turn, except for a cantrip with a casting time of 1 action.