The events take place in 1744 or 1745. The child that Louise de Rohen had with Charles Stuart was not born until 1748.
Jamie asks Claire if she knows what 69 was. In 1744 though that number didn't have a sexual connotation yet.
At Jamie and Claire's dinner party, Louise asks if anyone has attended Lully's opera Acis et Galatée. This work would have been considered ludicrously out-of-date in the 1740s, as it was first performed in 1686. Lully died in 1687.
When Clair's carriage is broken she says they will have to walk. However Paris has taxis from early 17th century and she surely should have been able to get one.