Just make sure you take into consideration that a lot of beaches in Europe are made up of rocks rather than the soft sand that most Americans are used to from many of our own beaches, Mexico or the Caribbean. Not saying you can't enjoy yourself, but if you have visions of lounging on a towel with your toes in the sand, you should do some advance research as to which beaches can offer you that (Nice is not one of those beaches). Otherwise, be prepared to rent a chaise lounge and invest in a good pair of the kind of sandals you can wear in rivers or oceans so you aren't stepping on sharp rocks along the shore, or under water as you try to make your way out to swim in deeper water.
If it is just a week, I would think about flying open jaw to Spain. Fly into Madrid for a few days, take a high speed train to Barcelona, fly home from Barcelona. You can enjoy 2 cities and have a little bit of beach time in Barcelona. If you want Italy, I'd also try for open jaw. Fly into Rome for a few days, head to Rimini for some beach time, move on to Venice and fly home from there.
If France is what you are wanting, consider basing yourself in Paris for the week and doing a few day trips by train (Versailles, Giverny, Rouen, etc.). If you don't care so much about beaches with pebbles and rocks instead of sand, you can forego the ultra touristy Nice for something like Dieppe which is just 2.5 hours by train from Paris. While not as hot as the French Riviera, in the summer months, it's still warm enough and you can have a full beach day but be back in Paris for a late dinner and some nightlife.
