The 44-year-old Pires was a member of the French side and team mate of current national manager Didier Deschamps that won the tournament for the first time at home in 1998.
They then won the Euro 2000 title and Pires said with his former captain in charge, there was no reason why the current side could not repeat the performance in the tournament that will be held across 12 cities in 2020.
"The Euro is the next opportunity for Deschamps. He has a very good team, a young team, very talented," Pires, who was in India as an ambassador for La Liga, told Reuters in an interview.
"Now everybody knows the names, the players. He can make a double of World and Euro champion.
"But it will be difficult because I think winning the Euro is more complicated, more difficult. But we have a good chance to win the trophy in two years."
Pires, who said he had a "good feeling" about the team's chances ahead of the tournament in Russia, recognised the similarities between his side and this generation's champions.
"I had a good feeling about the team this year," Pires said. "It was a bit similar between 1998 and this time. We had a good team, good manager, good young players.
"Didier Deschamps had a big role. Even in 1998, he had a big role. He was the captain. You need a player like him.
"Technically he's not so good but he was a warrior on the pitch."
POGBA CRUCIAL
One of the players that Deschamps will rely on is Manchester United midfielder Paul Pogba, who was instrumental in their World Cup run in Russia.
However, according to British media reports, Pogba's relationship with club manager Jose Mourinho has deteriorated after the player apparently criticised the side's tactics.
Pires said Pogba should try to repair his relationship with club manager Jose Mourinho, or at least make sure it was amenable and that he performed on the pitch.
"For Paul Pogba, the best is to say nothing," Pires said.
"He's a great player. If Man United paid a lot of money for him, it's because he's a good player.
"His relation with the manager may not be so good but he's a professional. It's very important for him to be focussed on Man United, on the pitch.
"Now say nothing, play football and walk out - that's my advice for Paul Pogba."
While Pires had acknowledged there were similarities between the team he played in and the current French side, there was no question who was the most talented.
"Sorry, no the current team was not better than us," he said. "The 1998 team was much better.
"We played with Zinedine Zidane and Youri Djorkaeff, the quality was very, very good."
(Editing by Greg Stutchbury)
