Well, this is exciting. A little more info here:
BEA Director Jean-Paul Troadec also told AFP that investigators have hope of finding the plane's black boxes because the debris area was relatively concentrated.
"The favourable news is that the debris area is relatively concentrated. And this gives us hope of finding the black boxes," he said.
Troadec said the parts of the wreckage that had been found consisted of "engines and certain elements of the wings".
The BEA is to publish first pictures of the wreckage found in the Atlantic on Monday.
"The BEA will on Monday afternoon hold a press conference to show first pictures of the plane parts," a spokeswoman told AFP.
The conference is to be held at 3:00 pm (1300 GMT) at BEA headquarters near Le Bourget airport, north of Paris.
AFP: Parts of Rio-Paris jet wreckage found