rester

to stay; to remain, be left over; to stay, to remain (to continue to have a particular quality); to rest; to live

“On est restés à l'hôtel pendant une bonne part du séjour, on était tous malades.” — We stayed at the hotel for a good part of the trip, we were all sick.

From Middle French rester, from Old French rester, from Latin restāre. According to the Trésor informatisé, the Old French is a borrowing from Latin. What speaks in favour of this is the preservation of [st], which in a popular word should be simplified to [t] (yielding modern *rêter). Alternatively it could be inherited, but influenced by the Latin.