Third-ranked France bounced back from a shock defeat to Colombia by whipping Mexico 5-0 in Ottawa to finish top of Group F with six points.
England, also on six points, but behind France on goal difference, beat Colombia 2-1 in Montreal and advance second from the group.
The 28th-ranked South Americans also advance past the group stage for the first time with four points from three games as 15th-ranked Mexico are on their way home with one point.
"A loss today would have sent us home. We've achieved our first objective, we can breath a bit easier now."
France are bidding for their first title after finishing fourth in Germany in 2011 and also at the 2012 Olympics.
France's Marie Laure Delie scored after just 34 seconds in an early goal blitz that saw Eugenie Le Sommer net a double and an own goal by Mexican defender Jennifer Ruiz.
"We were favourites but I've enough experience to know that things can go terribly wrong in football," said Bergeroo.
"We've a lot of humility because France have never won anything. We've simply closed the gap on the best."
Mexico coach Leonardo Cuellar's side go home for the third time after the group stage, with a point following their opening draw against Colombia.
"There was a lot of pressure on this young team who had to deal with great expectations in our country," he said.
"Conceding a goal after 30 seconds complicated things. France are a great team but we were far from what we had hoped for.
