Kylian Mbappé's second-half penalty secured a hard-fought 1-0 victory over Paraguay on Saturday, setting up a last-eight meeting with Morocco and keeping France firmly on course for a third World Cup triumph.
Speaking exclusively to Football Presse before the victory, Saha said France's success is no accident, insisting years of investment in player development, combined with the current generation's exceptional talent, have created an unprecedented period for French football.
"I think it's brilliant," Saha said.
"What we have managed to maintain in terms of quality, in terms of producing young talented players, is amazing.
"We have a manager with the national team who has really emphasised all of that."
Saha also believes the transformation of Paris Saint-Germain has played a major role in France's rise, arguing the club has helped create a winning mentality among the country's elite players.
"We had the chance to have the Qatar investment that built an enormous monster in PSG," he explained.
"That provides enormous confidence by playing in the Champions League with the best players and in the best competition."
Reflecting on the current state of French football, the former Manchester United and Everton forward believes no previous generation can match what the national team is achieving today.
"I think this is the greatest era in French football," he said. "We had a brilliant platform with Michel Platini, (Jean) Tigana and all those guys.
"They started the confidence journey.
"Then in my era, Clairefontaine was extremely important with players like Thierry Henry, Nicolas Anelka, William Gallas and many others.
"That then mixed with players like Patrick Vieira and Zinedine Zidane, who developed in the biggest leagues abroad."
"There are so many elements that have become a huge advantage for France."
While France have long been successful, Saha believes the current side has won over supporters because of the way they are playing, rather than simply because of their results.
"The emotions are really high," he told Football Presse on behalf of Freebets.com, the home of the best betting sites.
"It isn't only about winning. It's about how they play.
"For many years Didier Deschamps was criticised because people said his football was defensive, pragmatic and sometimes boring when you have that amount of talent.
"But now they are playing really well.
"The four forwards are extremely difficult to defend against. The whole defence also looks very steady and very strong. So it's great to see."
Saha also praised the spirit inside the France squad, believing Deschamps has struck the perfect balance between world-class individuals and collective responsibility.
"He has built something special," Saha said. "He understands there is talent everywhere in the squad. He made some strong decisions.
"He gave the captaincy to the best player, Kylian Mbappé. But he also told him to use the quality of players like Ousmane Dembélé.
"And behind them we have soldiers."
"That balance has become brilliant to watch."
With Mbappé continuing to lead France's charge after scoring the decisive goal against Paraguay, Saha believes his former international teammate deserves to be regarded among the very best players in world football.
"I think he is one of them," Saha said. "There are probably three or four Ballon d'Or contenders in this France squad.
"It's crazy.
"But Kylian has already played in three World Cups at his age.
"He has already broken records. You have to trust a player who has scored a hat-trick in a World Cup final."
"That tells you everything about his confidence."
Saha also reserved special praise for Dembélé, whose remarkable improvement over the past two seasons has surprised even him.
"Yes, it surprised everybody," he admitted. "People used to joke about him because he couldn't finish his dribbles or his chances.
"Now he is so efficient in the final third. He works so hard for the team.
"To become a Ballon d'Or winner and be respected around the world because of your work rate, even when you are so talented, shows unbelievable humility.
"The credit goes to Luis Enrique."
Saha believes France possess the ideal blend of youth, experience and quality to continue their World Cup journey.
"They have amazing balance," he said.
"In many tournaments the experienced players are already 33 or 34 years old."
"Our stars are 25 or 26.
"That is a huge advantage."