The verb déposer has many different meanings. Many of them refer to putting something down (i.e. putting something somewhere, so that you don’t have it anymore), as in the Latin deponere and the English deposit. In particular, déposer can mean to “deposit” some kind of request form, i.e. to file a request with an administration, e.g.

• déposer une demande … = file a request for …
• déposer une plainte contre quelqu’un = file suit against somebody
• déposer un brevet = file a patent
• marque déposée = registered trade mark

In this case, the mark refers to a design patent, or the French legal equivalent at the time. This is a legal monopoly on the appearance of an object, i.e. other people are not allowed to make an object with an identical appearance (or were not at the time the object was made). One files a dessin ou modèle: drawing or model, depending on whether the appearance is two-dimensional (e.g. the colors on a rug) or three-dimensional (e.g. a piece of furniture).

Thus, with these inscriptions, the manufacturer is signaling that they have registered a (limited-duration) monopoly on the design.