I am French, living in Lyon but with a very old house (clos de la Verrerie) in Autun. According to the archive of the house I have some information which could be useful for you.

In 1599 the property of the place was owned by Pierre Ballard (with two l)(archive départementales de Saone et Loire H1616)
In 1610 Pierre Ballard get for the Abbaye de Saint Andoche the champs Guillard (ibid H 812)
In 1650 the owner of La Verrerie is Jacques Balard, merchant in Autun (with one l)
when he died Mr Rabyot inherit from him (V reg de la catholicité)
The Ballard from Autun at that time are probably the ancestors of Balard dit Latour who is mentionned in several texts

Best regards

Diego Buriot
7 rue Camille Desmoulins
69007 Lyon France
E Mail diego.buriot@gmail.com