It is still not clear whether Marco Materazzi called Zinédine Zidane a "terrorist" or impugned the virtue of the French captain's mother or sister on Sunday night. He may have done all three.

"We'll only know if Zidane wants to tell us," said Vincent Duluc, who has covered the French team for the past decade for L'Équipe.

"It was certainly something like that," Duluc said, referring to the explanations offered for the headbutt which resulted in Zidane's expulsion from the World Cup final.

The French captain's agent, Alain Migliaccio, said Zidane had been provoked. "When he is calmer he will speak," Migliaccio promised. Zidane was "very sad" when he saw him at 2am, after France's defeat. "He didn't want to end his career like this . . . He is a person that doesn't say much but bottles it up and then one day explodes."

But Zidane smiled at the Élysée Palace in Paris, where he and the French team were invited to lunch yesterday. And he smiled later on the balcony of the Hotel Crillon, when he and the rest of the team waved at 10,000 supporters who gathered in the Place de la Concorde below them.

A giant, blue French jersey hung from the roof of the hotel. The players wore blue suits and ties. David Trézéguet, who missed a penalty, wept in the arms of Thierry Henry.

The Arsenal striker said: "All I want to say to Zizou, and I think France should say it and the world of football . . . is 'thank you', and 'thank you'. That's it."

President Chirac thanked the team for "making us live through unforgettable moments". By qualifying France for the World Cup final for the second time in eight years, Chirac said, "You have given us immense happiness, immense pride."

The French coach, Raymond Domenech, cancelled plans for a parade down the Champs Élysées, saying one does not celebrate a defeat.

"Of course I sense a certain sadness and disappointment among you, which I understand," Chirac told the team.

"The demi-god has remained human, by reacting to an insult," television presenter Michel Field said on LCI.

But other media were far more critical of Zizou. "Zidane has insulted other players in the past," Duluc of L'Équipe said. "Other players have complained about it. It happens all the time. In football, everyone tries to unhinge their adversary."

Duluc said Sunday night was the 14th time Zidane received a red card in his career. During the 1998 World Cup, Zidane was suspended for two matches after he wiped his feet on a Saudi Arabian opponent.

"He lost the Golden Ball in 2000 for a headbutt against a German player in the Champions League," Duluc said. "This is something that is part of him. He loses his sang-froid. He was wrong to react like that. He penalised his whole team. A champion must know how to control himself."

Le Monde's editorial also criticised Zidane. "With one blow, an icon has broken," they wrote. "A man placed on a pedestal by the whole country, the son of Algerians from Marseille, from humble origins, admired throughout the world because his story was like a fairy tale, has become through one gesture a bad example for the thousands of kids in the housing projects who dreamed of being a future 'Zizou'."

A young Arab inhabitant of la Castellane, the rough, immigrant neighbourhood of Marseille where Zidane grew up, told Le Monde that Zidane "may have forgotten us, but his headbutt showed la Castellane is still in him".

Despite his criticism of Zidane, Duluc said a positive image will remain. "People will remember that he got France to the World Cup final. The fascinating thing about this inglorious end is that, five minutes earlier, Zidane almost marked a second goal for the second time in a World Cup match (the first time was against Brazil in 1998), which would have put him up there with Pele among the all time greats.

"In France, no one wants to tear down the icon of Zidane," Duluc continued. "Everyone is stringing together explanations, excuses, justifications, based on the assumption that a guy as wonderful as Zidane couldn't do that without a good reason."

Domenech is set to be rewarded for leading France to the World Cup final by being offered a new contract to continue as coach.

His current deal expires at the end of this month, but the president of the French Football Federation, Jean-Pierre Escalettes, has hinted he wants Domenech to stay on.

Escalettes said: "For me, Raymond Domenech has not done a bad World Cup, he has actually done very well. I have always backed him up, and if the other members of the board think the same, then we will make the right decision."