European governing body UEFA has said it is unhappy about the state of pitches, in particular in Marseille, Lille and Saint Denis where the showcase Stade de France is located. It appeared to point the finger at stadium owners and clubs.
"I would like to tell our clubs that having nice pitches has to be their absolute priority," Le Graet told a news conference at France's training camp outside Paris.
"The quality of our pitches has to be better. We have great infrastructures but some of our pitches are not adapted to top-level football."
UEFA had asked for pitches in Nice, Marseille and Lille to be replaced, the FFF president said.
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"For Nice, it worked. For Marseille, it was more complicated but we have indications that it will be better for the matches to come. As for Lille, it is a failure," he said.
"Who's to blame? UEFA, the clubs? I think it's time to tell the clubs something needs to be done about this."
Almost halfway through the month-long, 24-team tournament, the demands on pitches have never been greater at a European Championship. Some stadia are hosting six games and wet weather across France is visibly having an impact.
With the exception of the Parc des Princes in Paris and Lens's Bollaert stadium, which are soccer-only venues, stadiums in the tournament have multiple uses as owners maximise commercial activity.
A French grass association accused UEFA of "scandalously" trying to pass the buck over the state of playing surfaces, laying the blame firmly on the governing body.
UEFA responded by saying it was entirely satisfied with the work done by its pitch consultant Richard Hayden.
(Writing by Patrick Vignal. Editing by Adrian Warner.)
