Replacement for an old FD-M760 front derailleur
Shimano used the same actuation ratio for all rear derailleurs up 9 speed on mountain bikes, and I'm pretty sure the same holds for front derailleurs. That means you can use any  8 or 9 speed front derailleur to replace a 9 speed M760.

I'd go with a FD-M4000 Alivio or FD-M3000 Acera if you want a new unit. Older 9 speed derailleurs will work if you can find one in good condition.

Note you'll need to match your mounting type: braze-on vs clamp-on; and top of bottom pull. If clamp on you'll need to know your down tube diameter and may need an adapter.