Does Green Flame Blade and Sweeping Attack combo cause the bonus effect of GFB to hit again?

The bouncing effect of green-flame blade will only trigger once

The green-flame blade spell states (emphasis mine):

As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range, otherwise the spell fails. On a hit, the target suffers the attack's normal effects, and green fire leaps from the target to a different creature of your choice that you can see within 5 feet of it. The second creature takes fire damage equal to your spellcasting ability modifier. [...]

The spell description constantly refers to a single creature that is the target of your melee attack and some different creature that is within 5 feet of them; thus, the spell has only one initial target. The Sweeping Attack Maneuver does not state anywhere that it increases the number of targets of a spell, only the attack itself. Green-flame blade will still only have one initial target so the bouncing effect only triggers once.

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Similarly, the extra damage on the attack will only apply to the first target

The green-flame blade spell goes on to states (emphasis mine):

[...] At 5th level, the melee attack deals an extra 1d8 fire damage to the target [...]

Because there is only that same one target, and Sweeping Attack does not add additional targets for the spell, the second creature would not even take the fire damage that the first one did.

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The Sweeping Attack Maneuver is weird

This feature states (emphasis mine):

When you hit a creature with a melee weapon attack, you can expend one superiority die to attempt to damage another creature with the same attack. Choose another creature within 5 feet of the original target and within your reach. If the original attack roll would hit the second creature, it takes damage equal to the number you roll on your superiority die. The damage is of the same type dealt by the original attack.

Reading this strictly we can conclude the following:

1. The Maneuver attempts to damage another creature using the same attack; it neither attempts to hit another creature nor does it involve a second attack of any sort.

2. You only damage the second creature if the original attack roll would hit them, not if it actually does hit them.

This feature is, at least to me, rather strange with all this wording. It makes for some weird instances where the second target has no effects on (dis)advantage or where critical hits only affect the first target, but that's how it is worded.

At my own tables I would quite likely rule the second target as actually having been hit by the attack, though I'd have to think more about the implications of that ruling before I made it.

No, GFB only triggers once

Greenflame blade description says

As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails. On a hit, ...

"On a hit" refers to the attack made as part of casting the spell, and the effect only applies to the spell's target if that attack hits.

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Additionally, Sweeping Attack is not even an attack, regardless of the name of the maneuver.

When you hit a creature with a melee weapon attack, you can expend one superiority die to attempt to damage another creature with the same attack. Choose another creature within 5 feet of the original target and within your reach. If the original attack roll would hit the second creature, it takes damage equal to the number you roll on your superiority die. The damage is of the same type dealt by the original attack.

It only deals damage to target.

"But it is 'the same attack' ..."

even if we liberally interpret the second 'hit' is an attack AND it hits, the spell only affect the spell's target, not the target(s) hit.

So, no, it will only trigger once.