French police in a statement Thursday described the remains as being in a "degraded state," Radio France Internationale reported. The body has been submerged thousands of feet below the surface.
Air France Flight 447 crashed en route from Rio de Janeiro to Paris June 1, 2009. All 228 crew and passengers on board died.
The plane's flight recorder was recovered this week.
A few bodies found floating in the Atlantic were recovered.
Relatives of those who died are pressing for recovery of all the bodies but experts say that may not be possible.
The police statement said the body recovered this week is onboard the search ship and a tissue sample has been sent to a lab for attempted identification by DNA.