As long as you have the legal right to work in France you may change jobs as often as you wish. However, if you resign from a position and don’t find work before your present carte de séjour expires you may find yourself in a bad situation. For many foreign workers, it is their contract which got them into the country and working legally in the first place. The ideal situation is to find a new job before leaving the old position, otherwise you may find yourself without a job and a valid carte de séjour. If you do decide to leave your job before finding another position, time it so you leave immediately after you have renewed your carte de séjour.

Generally, people don’t move from job to job and the notion that there is always something better, more money to be made, or more to achieve is not part of the national attitude, so you may find it quite difficult to change careers or even to change sectors.