The Hôtel de Ville (town hall) of Le Mans occupies the site of the Palace of the Counts of Maine within the old city walls, incorporating medieval towers and masonry into a building that was largely rebuilt in the 17th and 18th centuries. The result is an interesting palimpsest: you can see where Renaissance additions were grafted onto medieval stonework.
The building faces a small square at the top of the old town that makes for a good orientation point when exploring the Cité Plantagenêt. The exterior is freely viewable and the square is a pleasant place to rest before descending the steep medieval streets toward the cathedral or the lower town.