In short, very little.
The city was badly battered as it was, near enough, the pivot point for the US forces to swing north towards the Falaise gap, closing the trap for the German forces trapped in the 'pocket'.
Depending on what direction you take to get to Le Mans, you may be riding through (or close to) the D-Day landing sites and into the boccage, scene of the most desperate battles. Far more soldiers died in the days
after D-Day than during the actual landings, of course. Indeed, the subsequent slaughter outmatched that of the eastern front over a comparable period.
Antony Beevor's (excellent) new book should give you at least a spirit of the areas you may be passing through:
PS WW1 was fought out way to the east!
PPS A bit away from Le Mans, but not impossible, would be the U-Boat pens on the Atlantic coast, perhaps?