[RPG] Does Green-Flame Blade qualify for learning from Spell Sniper

I would allow it, but since as you say, Produce Flame does not in fact "require" the attack roll, I would say RAW you could not choose it.

RAI, I think it works -- if you want to attack with Produce Flame you make an attack roll rather than having the target make a save (or just get auto-hit, as with Magic Missile). So RAI, since Produce Flame is one of the type of spells that Spell Sniper works well with, I think it's a valid choice.

It is possible by taking a feat

As Dungarth explains, the range of the spell limits the caster to use the weapon attack on a creature within range of the spell.

The range of Green Flame Blade is 5 ft, and requires the caster to make an attack roll with your weapon, so even though the range of your weapon is 10 ft, the spell's restriction still applies. BUT, read the first bullet of the Spell Sniper feat:

When you cast a spell that requires you to make an attack roll, the spell's range is doubled.

That means that, if you take the Spell Sniper feat, a target is in fact in range at up to 10 ft, meaning that you can utilize any reach weapon with the spell. However, the secondary target of the spell must still be within 5 ft of the original target, as the restriction is not based on the range of the spell.

Update: Jeremy Crawford has confirmed on twitter that it works: https://twitter.com/JeremyECrawford/status/663511408269627392