Of course you can carry a purse,, look around, most women do.
What you will not do is keep your passport in it, or any large sums of money or credit cards. A money belt for those items.
Some of the men on here are anti purses. I have no idea why . Sigh,, I think they are jealous really, perhaps a secret longing to carry a purse,, LOL
Yes, purse should have a zipper. Better yet a bag you can wear across chest( messenger bag style) that has a zipper and a flap that buckles over the top .
Pickpocketing happens in most touristy areas( I mean all over Europe, not just in Antibes) , do not be freaked out about it, just be aware. In any crowded area try to keep as far away from people as you can,, meaning, on a subway , bus, train station area, beaware if anyone is standing near enough to touch you. Keep you hand on your purse, do not , ever, loop purse over chair back at a restaurant, do not put on floor, nor on top of a table if you are sitting outside( where someone could literally snatch it and run into a crowd).
Do not assess money belt in public, go to a washroom , or if desperate at least stand back with a friend blocking view. You do not need to tip anyone off where the money is. You should have a bit in your purse for lunch and extras.
Worst case scenerio is you lose a good lipstick ,, since your purse should only have spending money for one day in it. Rest of stuff in moneybelt, or if they have safes provided for lock up, I have no idea what your sleeping arrangements are. Do not lock money in a suitcase and leave in room. Suitcases are portable. Moneybelt or safe.
You will be fine, its going to be so fun, you will never forget this trip. Go with an open mind.. be prepared for many things to be different.
Be aware, but not paranoid.
Have a fun trip.