I wonder if she simply sees that you are the enemy because when you are there, Mommy and Daddy go away or she has to go to school, and isn't handling it well. How do Mom and Dad prepare her for the day apart? It may be a cultural difference, but I try to keep good byes short but positive with DD. When you pick her up, is she just disappointed that it's not Mommy? I would get down on her level and be cheerful and remind her that you picking her up means that you and she will have fun at home and Mommy will be home soon. And then I'd literally pick her up and carry her out if she throws a fit. Grab her bag (or use a backpack so you can carry her) and out you go, no nonsense. If you think she is hungry, pack a healthy snack that she likes (raisins are a hit with my DD).
Do you know about the book The Kissing Hand? It's at least offered in Canadian French. I'd talk to the parents about them reading it to her and giving her a kissing hand to take to school with her. It's been a good book for my DD who recently started preschool. http://www.audreypenn.com/kissinghand.html
I also think that going suddenly from Mom and Dad to full day school and a nanny is a lot for her so she may need more time and assurances to adjust.
You might also talk to the parents about what they want from you when you are all together. Tell them that she easily gets over her tantrum when they leave and is adjusting well, so that the hitting isn't their only impression of your time together. Or, since it's directed at you, tell her - in French - that it's not nice to hit people.
Remember, too, that 3s want a little independence, so figure out what she can do and what she can't. Can she climb into the seat but you do the buckles? Can she choose her shoes from 2 pairs offered? Can she pour milk if you give her a smaller container? Or could she be happy helping you by getting a cup from a low cabinet? Try giving her limited choices and see if she responds positively.