The Persian Gulf is a key route for oil tankers, while container shipping companies often use the Suez canal route.
CMA CGM stopped services in Iran last year in light of U.S. sanctions but company chairman and CEO Rodolphe Saade said CMA CGM was still sailing through the Persian Gulf.
"We are continuing to go there," Saade told reporters at a business conference in Aix-en-Provence.
Asked if CMA CGM had stepped up security on vessels going through the Persian Gulf, Saade replied: "No, because the measures we have in place are already sufficiently elevated."
Iran said on Sunday that it was fully prepared to enrich uranium at any level and with any amount, in defiance of U.S. efforts to squeeze the country with sanctions and force it to renegotiate a 2015 nuclear deal with world powers.
Earlier in the week, an Iranian Revolutionary Guards commander threatened to seize a British ship in retaliation for the capture of an Iranian supertanker by Royal Marines in Gibraltar.
Major shipping companies such as A.P. Moller-Maersk, Mediterranean Shipping Co (MSC), CMA CGM and German container group Hapag-Lloyd all informed customers this week that they would raise prices on Gulf-bound containers.
Saade added on Sunday that CMA CGM's overall volumes of business were good, despite the impact of tensions in the Middle East and a trade dispute between the United States and China.
In May, CMA CGM reported a first-quarter net loss of $43 million, although group sales surged 36.9% to $7.41 billion, as earnings were impacted by slowing China-U.S. trade and higher lease costs.
(Reporting by Sudip Kar-Gupta; Editing by Sarah White and Elaine Hardcastle)
By Sudip Kar-Gupta