The "FRANCE" mark is moulded indeed in the glass. See photo.
The "Verrerie de Bayel"exists since 1666, located in the northeast of France. It is mentioned in "Glass Fact File A-Z" of Ivo Haanstra.
I have 3 ring holders of BAYEL. All 3 marked BAYEL , moulded in the glass. They made several trinket sets, some of them look like the famous Baccarat Bambou Torsé sets but the quality of the glass/crystal is quiet different. Baccarat is of course the best one.... You see and feel immediately the difference.
If you use the French words : verrerie, verre moulé, verre pressé, ensemble de toilette, garniture de toilette, baguier etc. you will find your way.