Judicial investigators know the part comes from a Boeing 777, but they say they still need to identify a number inside the wing part, called a flaperon, the source said.
When the flaperon washed up on Reunion island, a French territory, its discovery was considered possibly the first physical evidence that might help shed light on one of the world's greatest aviation mysteries.
Authorities have not been able to explain why the jet veered dramatically off course during a scheduled flight from Kuala Lumpur to Beijing on March 8, 2014, or to say where exactly its errant journey ended.
Though French authorities have not yet confirmed it, Malaysian Prime Minister Najib Razak said earlier this month the flaperon does, in fact, come from MH370.
The part was transferred to a lab in Toulouse for inspection.
Martine Del Bono, spokesperson for the French BEA (Bureau d'Enquêtes et d'Analyses) -- the government agency in charge of investigating aviation accidents -- said there were two investigations in France: one by the BEA about how to improve security on planes and a judicial investigation on whom to blame for the crash.
"Experts still haven't determined the causes of the MH370 accident," she said. "The flaperon isn't enough. We need more. We need to localize the wreckage. It is extremely crucial in order to determine what happened."
"BEA investigators helped with the searches on Reunion Island and Maldives but we couldn't find any more debris so we stopped the searches.
"There are strong indications that this flaperon is from MH370, but we are still unsure. We are still missing identification from the parts list in order to fully confirm it is from MH370."
A source close to the investigation told CNN, "What we know so far is that it is for sure from a 777. We know that this is the only 777 that is missing in that specific region.
"We still need to identify a number that is inside the flaperon. It is a Spanish subcontracting company that owns that part. This company would be able to identify this number, but the staff is on vacation. We'll have to wait for next week to get their guidance.
"Judicial experts gave a preliminary report to the Paris prosecutor's in the meantime."