During war or crisis, evacuation flights for emergency purposes usually organized by governments. However, those are intended for citizens of that country. For example, there were evacuation flights intended for French citizens stuck in the UAE during the initial stages of the Iran war following a drone attack, but what happens if the traveler has both a French & American passport? Which government takes charge on the situation?

Evacuation is straight forward when the person only has one nationality rather than two since that nation only ensures their safety & rescue while someone with two passports: let's say both the US & France want this person out of the danger zone, but who takes the sole responsibility if both countries want the same thing? It can't do both, has to be one or the other even if the French plane arrived first before the American one.