Have you looked at monumentaltrees.com? When we’re going to a new area, we’ll look up the name of the department to see what’s where. We’ll go slightly out of our way to see a special tree. I have to admit that the tallest/widest/oldest may turn out to be a damaged or scraggly tree.
Chartres itself is on a flat plain, but just to the west is the hilly, wooded region of the Perche in the Orne department. There are some fine forests here and some wonderful trees. My favorite is the pair of plane trees in L’Aigle at the Square Eugène Pasquis, Rue Marcel Guiet. These are probably the most magnificent trees I’ve seen in France.
Near Belleme there is a forest around a beautiful lake, L’etang de la Herse, with walks leading up into the hills. There are more large forests just west of Belleme, which hosts an internationally known mushroom event in the fall. Near La Perriere is the very tall Chene de l’ecole, born in 1666. There’s an oak near Pervencheres (le chêne de la Lambonnière) that’s worth a look. You can drive to all of these, though I understand you also want to walk in old forests. Near Belleme you can drive into any forest, park off the road, and walk in any direction. These are all in the Perche region of the Orne.
France is proud of its national forests. In Pennsylvania we’re also proud of our forests and find French state forests a little bland, a little too well managed in our opinion. But because of centuries of good management, when they were looking for the tallest straightest timbers to replace the tabouret at Notre Dame after the fire, they found them in the Perche and the Sarthe.
I should also mention that an hour or so west of Chartres is the town of Senonches, which has a forestry museum in its old chateau. My husband was fascinated.
Just wanted to add that there's a long allee of plane trees lining the road as you approach Belleme from the north, as well as a shorter allee leaving Belleme to the west.
You'll be going through the Mayenne department on the way to Rennes. We love both landscapes, the Perche and the Mayenne, but our favorite thing to do in France is walk the former towpath along the Mayenne river, with some wonderful old trees along the path. Also in the town of Laval is a park with sequoias, magnolias, and oaks (Jardin de Perrine) and a view of the old chateau and the river.