Upgrading stock front derailleur - Will Shimano Deore work with 3x7 gearing?
A 10-speed FD will not work well. Mismatching FD "speeds" (inner cage width) with chain width usually gives poor results in either direction. In this case you would probably find it's impossible to get it to not rub somewhere. Just get a 7/8-speed Altus, FD-M313 for the current one. It will easily meet the goal you describe and play nice with the rest of the drivetrain without having to mess with anything else.