The French high commission said the Air Tahiti Nui chartered plane was carrying, apart from freight, returning residents and members of the mobile police team who would be quarantined in the barracks.
Four more such flights are scheduled until the end of June, when scheduled air services are expected to resume.
Hundreds of residents remain stranded in France, with no further plans to speed up their return.
Meanwhile, the government eased restrictions on liquor sales so that the wine store and designated liquor outlets can open, except on Sunday afternoon.
The territory recorded 89 positive tests for Covid-19 but keeps two counts, the 29 Ecuadorians tested at Nuku Hiva this week being listed as cases of transit because most of them are on their fishing boat off Tahiti.
One of the Ecuadorians was flown from Nuku Hiva to the hospital in Tahiti where he is in intensive care.