No, Cholet Le Pontreau Airport (CET) does not have a lounge, and asking a Cholet airport lounge question is really asking about the wrong kind of airport. Cholet Le Pontreau is a general-aviation aerodrome west of Cholet in the Pays de la Loire region, built for flying clubs, gliding, and light aircraft rather than scheduled commercial service, so there is no passenger terminal lounge to search for here.
The reason runs deeper than size. Cholet Le Pontreau has no scheduled airline flights at all, which is the real explanation for the missing lounge: a lounge exists to serve ticketed passengers waiting between check-in and boarding, and that entire category of traveller simply does not pass through this aerodrome. What you find instead is a clubhouse culture built around private pilots, students, and weekend flying rather than any airline-facing infrastructure.
For anyone actually flying commercially out of this part of western France, Nantes Atlantique Airport (NTE) is the real answer to a lounge question. Nantes is the region's scheduled-service hub, roughly an hour's drive from Cholet, and it carries the kind of airline and card-network lounge options that a field like Cholet Le Pontreau was never built to offer. If your itinerary starts near Cholet but your flight departs from a commercial terminal, Nantes is where any lounge planning belongs.
There is no workaround to suggest at Cholet Le Pontreau itself, no day-pass counter or quiet corner marketed as a lounge, because the aerodrome was never designed around that kind of passenger flow. Pilots and their guests use the clubhouse and briefing rooms rather than anything resembling a commercial lounge. If you searched for this airport by name expecting an airline gateway, the honest redirection is toward Nantes Atlantique for both the flight and any lounge access you need, rather than treating Cholet Le Pontreau as a miniature version of a hub it was never meant to be.