We've an early morning 7am flight from Nice airport. Are there any gas stations close to Nice airport which are open around 5-5.30am and you can use your credit card to fill up the gas.
Yes there is a TOTAL gas station in the airport, just near the renter's agencies.
You can locate it on a map or have the full description on the TOTAL website. It says it opens from 6am, but in France most gas stations have at least one pump where you pay with a credit card open 24 hours a day.
Otherwise, you can pick any gas station on your way, as they are mostly open 24 hours a day for credit card holders (if you are returning the car to the renter and are worried about the tank being full, the needle usually stays at full for more than 10km after you completely fill up the tank).
Be careful with your credit card though, I know many gas stations refuse American Express for example. So the first time you go to a gas station, do within hours of operation to be able to pay with cash if your credit card does not work.
As you can drive quite a few km until the gas indicator shows less than full, and you won't arrive too late in Nice, you might fill up at one of the supermarkets, as it has been said. Most of them have lanes with a cashier during the opening hours of the supermarket, which is (unless it is a sunday) until 7:30 to 8 pm (definitely in the Nice area). So, you could fill up in the evening…
Also note about the supermarket gas stations, their prices are definitely lower than the ones at "regular" station (count 10 cents a liter), and even less than at highway rest stops (that may be up to 20 cents).
This website contains a list of 24h service stations in the 06 Alpes Maritimes department to which Nice belongs. Try seeing if any of the ones indicated are in fact on your planned route. Stations on private paying motorways are always opened 24h, either manned or automatised with credit card payments. Hence these are not shown on the aforementioned website.
Here is the full list of 24h service stations in France (from the same website), ordered by departments.
You will hardly find any petrol station in France that is not open 24/7 or does not accepts credit cards. It's paying with cash that has become difficult (and might be limited to certain times of the day). Unlike some other European countries where discount petrol stations only accept local debit cards, Visa and Mastercard-branded chip-and-pin cards should work anywhere.
A French peculiarity is that many out-of-town supermarkets have petrol stations under their own brand (and they have a large market share). Premium branded stand-alone petrol stations are therefore much less common than in other countries. Look for signs for supermarkets like Auchan, Carrefour, Leclerc, Casino, Intermarché, Super/Hyper U, etc. If a particular branch does have a petrol station, the signs will usually include a pictogram representing a petrol pump.
I used these many times and could always pay with my chip-and-pin card from another European countries (US cards that require a signature are another story, I never had to use one of those in France and I suspect it wouldn't be possible at unattended petrol stations).