All indications I can find are that you would be repatriated home or buried in France, though I can't tell how exactly the decision was made. Though Americans at the time worried about losing US citizenship if they served in the Legion, the law is open to interpretation. If you did not intend to take French citizenship or subvert US interests, then your service in a foreign army could be legal. Given that the US was fully supporting France in the Indochina War, it is likely that you would not face sanction.

If your body made it out of Indochina, and wasn't one of the many who went missing or died in prison camps, then it would go to France and perhaps onto your hometown. (Of course, tens of thousands of war dead were not repatriated and remain in Vietnam).

The French military has listings for several Americans who died in Indochina. Denis Joseph Domini was burried in Paris René Denis Victor Camborde was buried in Bordeaux. René Marguerite ROSAMOND has no listed burial.

Perhaps some of these men had French relatives and that accounts for their burial in France. But almost all were buried in France, the sample is too small to conclude a policy. However, when I check other nationalities, they are repatriated to their country of birth. So, my best guess is that yes, you would be repatriated if you wanted to, and you had family to accept your body.

You can see all of the listings for Americans who died in Indochina here: http://www.memoiredeshommes.sga.defense.gouv.fr/fr/arkotheque/client/mdh/guerre_indochine/resus_rech.php