The 41-year-old reflected on his success with France and believes Deschamps' impact was unrivalled, and underlines the differences between his former team and Spain
All three played a prominent role in France's World Cup and European Championship glory in 1998 and 2000, but Thuram believes the contribution of Deschamps is unparallelled to any other - even their famous number 10.
"Deschamps is a great coach. He was a great player, he has won everything and he knows what it takes to get to the top," he said.
"In World Cup 1998 and in Euro 2000, we had a genius in the form of Zidane, but the key was Didier."
Deschamps, now coach of the national team, welcomes Spain to Paris on Tuesday in a key World Cup qualifier which could determine who secures automatic World Cup qualification.
And Thuram, who ended his playing days in Barcelona, went on to highlight what he believes to be the fundamental difference between France and the European Champions.
"To play football and win, you need players who have can use their heads," Thuram said.
"When I arrived in Barcelona, I enjoyed playing with people balanced and normal: [Carles] Puyol, [Victor] Valdes [and Andres] Iniesta. This is because they are not footballers who think they are the centre of the world.
"The French, however, have forgotten how to be humble. The humility to understand that when you play for the France team, it is something much more important than your own self."