The golf at Mulsanne has competitions through the week on Wednesday through Friday so no chance of playing there. Le Mans Golfier is run by english people so no language barrier and is at Sargé lès le Mans, a couple of stops further round the ring road from the D338 north near Auchan. However, if it was me and I wanted to play an absolutely superb golf course, one of the best maintained in France, I'd go to Sablé, about 45 mins west from Le Mans. Built 20 years ago by a billionaire to amuse himself, it has 27 holes and a "compact" that would test the patience of a top pro. It has only 150 members and is truly manicured, always in top condition. To top it all, food to die for if you want the real restaurant and not the bar food (which is also excellent). As always in France, choose your own level of difficulty and tees. I play off 5 so am used to the back tees, but I'd advise the yellows if it is a fun round. They speak english.
Oh, but just a thought but you never heard it from me though. If, before the road closes on Thursday you go to the golf course at Mulksanne you could be locked in right on the bend for the practice later

There is a back road out which leads back to the Beauséjour roundabout too.