The green-flame blade spell cannot activate after missing with its attack
The spell's duration is "Instantaneous"
Firstly, the duration of green-flame blade is "instantaneous". What this means is that
The spell harms, heals, creates, or alters a creature or an object in a way that can't be dispelled, because its magic exists only for an instant."
Because of this, it would at least be unusual if the spell had an effect after it was cast (though some instantaneous spells do have lasting effects (such as feeblemind) so this isn't conclusive evidence on its own).
The spell does not indicate that it persists
We can compare the wording of green-flame blade to something like branding smite:
You brandish the weapon used in the spell's casting and make a melee attack with it against one creature within 5 feet of you. On a hit [...]
The next time you hit a creature with a weapon attack before this spell ends [...]
There are a few things to note here. First, branding smite has a duration of 1 minute and requires concentration, while green-flame blade does not. This indicates that the former can last after its initial casting while the latter cannot.
Second, branding smite occurs "the next time you hit a creature" whereas green-flame blade occurs on a hit with the attack that is made as part of the spell's casting. If it were intended to apply to attacks other than the one made when casting the spell, the spell would mention this fact similar to how branding smite does.
Lacking any text to support that green-flame blade has a lasting duration and lacking any text to support that it can activate on an attack besides the one made as part of the spell, we conclude that green-flame blade cannot activate with the attack from the haste spell.