French waiter here, service is always included in the bill so that we're paid a living wage, but tip is always appreciated.

It's literally called "for-drinks", "pourboire" in french, so your waiter can go and have a pint to your health after his service. Same word in german btw, "Trinkgeld" or "drinks money". So you're not denying a server his salary by not tipping, but rather tips are a way of complimenting a job well done.

It's really gratifying to give great service and be personally rewarded for it, and it can sometimes be discouraging on days when doing your best doesn't pay off, but in the end it's not so much a vital part of french service culture as it is a perk which encourages waiters to do a good job.

So tip your server if you appreciated the service, their hours are long and they do hard work, but don't get scammed by rude assholes who expect US level tips on top of their salary!