If I understand your question, mona is a name. There is no translation for the name mona. It would just remain the same name.
It's already a french word. It's one of the Mona Lisa's names.
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The Mona Lisa is called "La Joconde" in French.
"La Joconde" is how the French refer to "La Giocondo", or as I learned it ... "The Mona Lisa" I don't know if 'Joconde' is a French word or just the French pronunciation of Giocondo.
La Giaconda or the Mona Lisa
Mona Lisa was painted by Leonado DaVinci, who was from Florence (which is now in Italy) the painting is currently owned by the Louvre museum which means it is the property of the French government.
"Mona Lisa" is the English name for the famous Leonardo Da Vinci painting, which in Italian is "La Gioconda." The word 'mona' is a short form of the word 'madonna'.
"La Joconde"
the Mona Lisa is being housed in the Louvre Museum in Paris
La joconde
The French name for Leonardo Da Vinci's Mona Lisa.
Ma Lise as a personal reference and Mona Lisa as a masterpiece's title are French equivalents of the Italian phrase Mona Lisa. The respective pronunciations of the feminine singular possessive adjective and proper noun -- which references the painting by the world-respected genius Leonardo di ser Piero da Vinci (April 15, 1452 - May 2, 1519) and translates as "My Lisa" -- will be "ma leeze" in French and "MO-na LEE-sa" in French and Italian.