When your APS expires, you must change your status and request a residency permit adapted to your situation.
If you have an indefinite or fixed-time work contract validated by the DIRECCTE (Direction régionale des Entreprises, de la Concurrence, de la Consommation, du Travail et de l’Emploi - Regional Department of Competition, Consumption, Work and Employment) and are paid at least one and a half times the minimum wage (so approximately 2,220 Euros gross per month in 2017), you can request a temporary "employee" or "temporary worker" resident permit.
If you have created a company or developed an unpaid activity and you can prove the viability, you can request a temporary "freelance entrepreneur" resident permit or a multi-year "freelance entrepreneur - talent passport" resident permit for starting a company.
If you are engaged in research, you will be able to request a multi-year "researcher-talent passport" resident permit as a researcher.
Don't wait for your temporary resident permit to expire before you request a change of status. Do it as soon as your situation changes.