The RAI on this one is a little uncertain from what I can tell.
Jeremy Crawford responded here to a question about using Green-Flame Blade for AoO.
Without a feature like the War Caster feat, a spell can never be cast in place of an opportunity attack.
He doesn't make it incredibly clear, but the implication here is that with the feat this would be possible. However, this is contradicted by a later tweet here, stating that:
Twinned Spell doesn't work with a spell that targets more than 1 creature. Green-flame blade targets 2.
This explicitly states that the spell targets multiple creatures, and therefore doesn't qualify for the War Caster benefit, but again in a different context. My instinct here is to agree with explicit disqualification, rather than implied exception, so I would say the RAI is that you can't use Green-Flame Blade with an opportunity attack.