Louis, nicknamed "the wise", ruled France between 1461 and 1483, and it's thought the oil portrait dates from around 1470.
It is now valued at between 500,000 and 750,000 euros and is to be auctioned in London on 4 July.
The profile portrait shows Louis wearing the Order of Saint Michael chain around his neck.
The name of the artist, from the French School, is unknown, but the artwork bears an inscription, apparently added in the 19th century, detailing that Louis XI offered the portrait to his chamberlain and ambassador, Rigaud d'Aureille, Baron de Villaneuve.
Sotheby's classifies the painting as of "extraordinary historical importance", noting that until the 19th century, the painting remained in the collection of the Chateau de Villaneuve-Lembron, built by Baron de Villaneuve.