I've used
this site (you've got holidaylettings dot co in your post) a couple of times for short stay flats in London, and had success both times.
Since the website acts as an agent only it's the flat's owner which should be scrutinised carefully. If an owner wants payment by Western Union only then walk away, as that money can be collected from anywhere in the world. In the UK there are 'follow me' phone numbers (they start with 070) which can also be answered anywhere - less than honest people use them to advertise flats that may or may not exist. If there is a similar type of 'follow me' phone number in France then check to see if the owner's number fits that category.
As well, have a look at other websites to see what the average rate per night or for a week is for a flat in Nice. If the going rate for a flat for four people is €130 a night and you see one at the bargain rate of €40 a night it's likely not what it seems if it exists.
Check reviews at TripAdvisor and elsewhere, but take those which may say 'it was the most perfect flat ever' and 'it was the seventh level of Dante's inferno' with a large pinch of salt.
And if the information you receive seems sincere, if the owner replies to your emails promptly and the whole matter
feels right then take the plunge, book and hope for the best.