Alain Manesson Mallet; 1630-1706.

Precious little is known about this author, safe for having been a military engineer serving King Louis XIV.
His claim to fame comes from his very successful "Description de l'Univers", a pocket size thick geography book in five volumes, replete with encyclopedic details, historical data, scores of illustrations (landscapes, decisive battle scenes, towns, forts, harbors, .), and quite a few simple maps.
The book was published between 1683 and 1688.
However, reprints were made later with German text (1686 and 1719).
Of note also his "Les Travaux de Mars" in 1672 on the art of fortification, and "La Géométrie Pratique" in 1702, a massive study in geometry, trigonometry, planimetry and land survey.

Floride.

This small and minimalist map (4 ½" X 5 15/16") was designed for the 1683 "Description de l'univers". In a confused way it shows that, boxed in by New Mexico on the west, Canada on the north and Virginia on the north east, there was a huge "Florida" territory made up of areas such as Apalache, Cossa and Tegesta (so named after the Tequesta tribe living at that time in present days east Florida). No mention is made of Louisiana, since it had just been explored by Cavelier de la Salle who paddled down the Spiritu Santo River (Mississippi) in 1682 and had not yet had time to walk back up to Montreal and return to France to claim the whole Mississippi basin for his King.
Notice that only two towns are indicated: St. Augustine, and north of it St. Mathieu (San Mateo was the settlement built by the Spaniards on the ruins of the French Huguenot Fort Caroline which was destroyed in 1565.
Typically the St John River (known then as the River of May because it had been discovered by Captain Jean Ribault on May 1st 1562) has its source in a substantial fantasy lake.
Note that the peninsula coastal delineation is much influenced by the 1657 Sanson's seminal map of the area.
French text on verso.