A permanent residence visa in France allows you to stay in the country for ten years. Because it is renewable, you may theoretically live in France permanently with this status. While you have many of the same rights as French citizens, you do not have all of them. You can’t vote in elections or occupy public office, for example.
If you choose to become a French citizen, you will also become a member of the European Union. As a result, you have complete freedom of movement throughout the EU. If you become a French citizen, you do not have to give up your original nationality; you can have dual citizenship.