While I'm able to find some 20th century French artists with this last name, I'm unable to find "LOUBET" in mid-late 1700s, the point in time when this young French woman's portrait was done. Her fashion and hair puts her squarely in the era leading up to and through reign of King Louis XVI and Marie-Antoinette. I tend to think this is c.1750s-70s. Little notations on backside don't tell us anything important, but seem to be collectors' notation through the 250+ years since. Full measurements are noted on the photos.
Very good to excellent condition for age and type, she is painted in gouache on thin wafer, typical of the genre and era. The painting and wafer have no hairlines, no chips, really no flaws to note. The artist's signature is visible, which normally meant it was an artist of some fame or standing in his or her time. Frame is fine, might have a layer of gold or perhaps the thin 18k plaque we often see in portraits of this period. I can see the bonded layer on the edge, but I have not acid tested this one. There is no warp or flaking on the little painting other than one tiny white spot on her bodice. You can see the old original foil remains behind the painting wafer - this is meant to draw and reflect light through the skin tones.