Like people said TF3 only makes sense after TF2 has lost all interest and the economy is dead. It could be 5 or even 10 years before that happens but it's fun to think about what TF3 could be, no? Personally I'm thinking the cartoony artstyle is a staple and should stay, but it could be made in a futuristic setup instead of 60's-70's action espionage movies.
Gameplay-wise I'd like it to come a bit closer to arena shooters and play faster, which could be overall increased movement speed, maybe strafe jumps and/or quickdodges, maybe even friggin jetpacks, who knows.
You'd also need to change the support classes. Changing pyro to a LG class that has a projectile shield instead of airblast, heavy to be a half-tank half-support but not really dealing that much damage, engie maybe emphasised in quick teleporters and supplying buffs (armor/damage/etc) to his teammates instead of sentries, medic with a bit more combat ability but a heavy nerf on the ubercharge mechanic so it isn't so central to the gameplay. Like ideally you'd be able to choose to have a medic or an engie as your support without much difference.
Other classes could be more or less the same as they are. Possibly make the spy still able to backstab but more revolver-based with better guns, as stabbing won't be as effective with everyone wheezing around the map at quake-like speeds.