I thought you meant the pit/paddock area....
If you indeed mean scrutineering in town, it is like GT6 mentioned on Sunday and Monday at the beginning of race-week in the town centre, at Place de la Republique. I'm not sure you can buy tickets to go in the inner-circle, but as an ACO member you can take a free guided tour which takes you inside. I then sneak off to take pictures and leave the guide and my fellow tour-members alone because a) I am not that fluent in French and b) know more about Le Mans than the guide anyway....
I often take that tour twice on the Sunday, and twice on the Monday
