Talks with the management of Elengy, the LNG branch of GDF Suez, restarted on Friday morning after a meeting on Thursday failed to end the dispute.
"The three LNG terminals which belong to GDF Suez have now all stopped operating," the CGT union said in a press release.
"Talks restarted today at 1000 (0800 GMT). A positive outcome to a situation which has lasted much too long is reachable," the union added.
The workers demand a raise in their annual bonus to reflect the companies' higher profits, a CGT union official said.
One of two liquefied natural gas (LNG) tankers blocked by workers in the southern French ports of Fos Cavaou and Fos Tonkin has been diverted to Spain after it was unable to unload due to strike action, ship tracking data showed.
The Qatari LNG vessel Al Gharrafa, which can carry up to 216,000 cubic metres of the super-cooled fuel, is expected to arrive at the southern Spanish port of Algeciras on Saturday, AIS Live ship tracking data on Reuters showed.
The ship was last seen off the coast of Valencia at 0520 GMT on Friday, after it was still anchored off the French coast on Thursday, according to the tracking data.
Workers announced strike action on Tuesday, refusing to unload the Al Gharaffa and Cheick Bouamama tankers, as well as an LNG delivery to the northern French terminal of Montoir.
The 150,000 cubic metre Grace Cosmos LNG tanker is due to deliver a cargo to Montoir on April 23, AIS data showed.
French LNG workers last downed tools for two weeks in autumn 2010 as part of wider strike opposing pension reforms.