Fifty-six percent of respondents said they backed the government, while 42 percent said it should have offered to let the ship dock, according to the OpinionWay poll.
The Aquarius, run by French charity SOS Mediterranee, was eventually allowed to dock in Spain on Sunday after being stranded for days while both Italy and Malta refused to let the migrants ashore.
Local leaders on the French island of Corsica had offered to welcome the Aquarius, but the move was slapped down by the central government, which argued that under international law the ship had to dock at the closest port.
- First Aquarius migrants arrive to cheers in Spain
- 'I never meant to offend you': Macron tries to smooth over migrant row with Italy
Tensions flared after President Emmanuel Macron accused Rome of “irresponsibility”, although he later said he had not meant to offend France's southern neighbour.
Macron is under pressure to close down migration routes from Africa amid strong anti-immigration sentiment in his country.
France has said it will examine asylum requests from Aquarius migrants who want to come over from Spain on a “case-by-case basis”, government spokesman Benjamin Griveaux said Sunday, although he did not know how many might make the requests.
Rome's decision put the migrant influx back to the fore ahead of a EU summit on June 28-29, where leaders are supposed to hammer out an overhaul of
the bloc's asylum rules.
The OpinionWay poll was carried out among 1,020 adults online from June 13-15.