Provins is open year-round but the medieval shows (jousting and falconry) only run from Easter to early November. If those are part of your plan, time the visit accordingly.
The single best weekend of the year is Les Médiévales, the annual medieval festival in early June. Around 130,000 visitors over two days fill the upper town in period costume — knights, jugglers, falconers, blacksmiths, weavers — for a remarkably committed reenactment of the great Champagne fairs. Tickets sell out in advance and accommodation in town disappears quickly; book ahead.
Outside the festival, late spring and early autumn offer the most comfortable weather and the fewest tour buses. Summer weekends are busy with day-trippers from Paris; weekdays even in July are noticeably quieter. Winter is quiet but several monuments operate on shorter hours and a few of the smaller museums close entirely between November and Easter.