The CMA CGM Kribi, sailing under a Maltese flag, departed waters near Dubai and transited the strait on Thursday.
By Friday morning it was located near Muscat, Oman's capital.
During the voyage, the ship signalled its owner was French.
The shipping company and France's foreign ministry declined to comment.
According to Bloomberg, three other vessels also appeared to have passed through the strait on Thursday.
The UN Security Council on Thursday postponed a vote on authorising the use of "defensive" force to protect shipping in the strait from Iranian attacks.
France has been sceptical of military action, with President Emmanuel Macron previously calling an operation to reopen the waterway "unrealistic".
Iran's near-closure of the strait has caused a significant rise in oil prices.
The waterway normally carries around a fifth of the world's oil shipments.
(ał)
Source: Bloomberg, PAP