"The boat is surrounded by at least three Israeli ships and since 9:06 am (0706 GMT) all the communications have been jammed. We can't get in touch with them by phone or by internet," Julien Rivoire said by phone from Paris.
The Israeli military refused to confirm that its ships had approached or intercepted the vessel, which is carrying 16 people, including three crew members and three journalists.
"All I can say for now is that we're monitoring the boat," a military spokesman told AFP.
Earlier on Tuesday, Rivoire told AFP the boat was not expected to reach Gaza before noon.
"The boat, which is moving slowly in a calm sea, should arrive in around five or six hours, which would be around midday, at the Gaza coast," he said.
Activists on board the ship tweeting in both French and English at @BateauGazaFr, had earlier announced that the Dignite/Al Karama was heading for Gaza after spending the night anchored at sea.
"We're cleaning ourselves up a little bit before arriving. Morale here is like the sky and sea -- very good," wrote French activists on board, adding in English: "Gaza, off we go, stay connected!!!"
Israel has said it will not allow the boat, which was originally part of a 10-ship flotilla, to reach the Palestinian territory in violation of its naval blockade on Gaza.
On Monday, Israeli deputy foreign minister Danny Ayalon said the Jewish state would prevent any attempt to breach the naval blockade on Gaza.
"If this boat is on its way to Gaza, which is a breach of international maritime law, and tries a provocative act -- yes, we shall intercept it," he told reporters in Jerusalem.
"But I assure you we shall try our best to make those on board very comfortable."
Israel maintains that its blockade of Gaza is legal and necessary to prevent the Hamas militant group that controls the territory from obtaining weapons and funds.
But French activist Thomas Sommer-Houdeville, reached on board the boat on Monday evening, said the vessel was only carrying a "symbolic message of peace and hope and love" and that Israel had no reason to intercept it.
"We hope that they will not, we don't have a plan but we have a peaceful humanitarian mission. We are a peaceful boat flying a French flag."