Stephanie Foray, a 30-year-old civil servant, had arrived in Malaysia on May 5 and went missing shortly after taking a ferry five days later to Tioman island off the east coast of peninsular Malaysia, according to Malaysian media.
Police last week said they had arrested two Malaysian men over her disappearance.
Johari Jahaya, chief of the police district with jurisdiction over Tioman, told AFP that police discovered the skeletal remains on the island on Monday.
"I can confirm that we have found a skeleton on the island and we are now getting a DNA test to see if it is actually that of the French woman," he said, declining further comment.
The New Straits Times newspaper quoted T. Narenasegaran, head of criminal investigations for Pahang state, of which Tioman is part, as saying the remains had been buried in a cave.
Police were led to the site by one of the two detained suspects.
"We then found some clothes which we believe were Foray's before the suspect pointed to the spot where the remains were buried," he told the paper.
"After digging for about four hours, and at a depth of about three metres, we found a mattress. Below it were the remains. The skeletal remains were intact," he said.
Foray left France in November last year on a holiday that took her to India and Sri Lanka before she arrived in Malaysia.
Her family lost contact with her three days later, with the French embassy subsequently putting out a missing persons alert. Embassy officials have declined comment on the case.
The New Straits Times previously reported the two men arrested were the 44-year-old owner of a Tioman chalet and his cousin.