Somewhat uniquely, in France this doesn’t matter.

French courts can fully convict in absentia, and they ignore several treaties. For example, a person cleared of murder in Ireland can be trialled subsequently in France, convicted with no participation (or no facilitation of participation from abroad), and incredibly an extradition request to Ireland for someone Ireland did not jail for the same alleged crime.

Ireland did not extradite the accused and the situation was resolved only by the accused’s death.

France could quite well convict Musk and then fish for extraditions from every country he visits.