The Daily Show host made the comments on his satirical show a day after France beat Croatia to win football's most coveted prize on Sunday.
More than half of the French squad can trace their heritage back to Africa.
The French ambassador to the US said the comedian was denying their "Frenchness" by calling them African.
"This, even in jest, legitimises the ideology which claims whiteness as the only definition of being French," Gérard Araud said in a stern letter to Noah.
"They were educated in France, they learned to play soccer in France, and they are French citizens. They are proud of their country, France."
The Daily Show posted a video of the South African comic reading out the letter on Wednesday (later tweeted by the French embassy in the US) - and going on to argue that the players' African identity should be celebrated.
Noah said he understood where the ambassador was coming from and how his comment could be perceived as "joining the attack" with France's far right.
But he said his statement should be put in context: "When I am saying, 'They are African', I am not saying it as a way to exclude them from their Frenchness, but using it as a way to include them in my Africanness."
To deny that duality was something he "vehemently" disagreed with.
By Lucy Williamson, BBC Paris correspondent
France's last World Cup win in 1998 triggered a national debate over French identity, after the slogan Black-Blanc-Beur (Black, White, Arab) was coined to describe the multi-ethnic team. It was a striking development, because discussing race or religion is officially considered irrelevant to French identity - even frowned upon.
The French state collects no data on the ethnic origins of its citizens; a way of underlining the principle that all are equal, and equally French. The reality is somewhat less "colour-blind", though, according to many of those who come from immigrant backgrounds, and especially from France's former colonies in Africa. They say many areas of French life - such as getting a job - are more difficult with an immigrant name or a non-white face.
France's colonial past has left uncomfortable divisions here; divisions which have been exacerbated by city planning around its major cities, and - some would say - a Republican ideal that is often seen as rooted in France's white Christian history. The recent debate around the place of Islam has highlighted these tensions again.
The national squad is still a rare symbol of multicultural France, but 20 years on from their last World Cup win, the image of a team from many different backgrounds has triggered less focus on French identity here and more wry comment on the country's current stance on immigration.
The feud comes after Khaled Beydoun, a US author on Islamophobia, called in a Twitter post for "justice" for Africans and Muslims in France because they "delivered you a second World Cup".
The tweet was widely shared and garnered criticism and praise. Some were worried it would hamper race relations in a country that had witnessed its political discourse become inflamed following a migration crisis and a number of terrorist attacks.
Earlier in the week, Noah had also posted to his Instagram account a cartoon by M Rifai showing a boat full of migrants handing the World Cup trophy to France.
In his letter, Mr Araud stressed that the players "rich and varied backgrounds is a reflection of France's diversity", to which Mr Noah replied: "Now I am not trying to be an asshole but I think it is more of a reflection of France's colonialism."
France's founding principles and universal values means it does not collect data or statistics on its racial, ethnic or religious backgrounds.
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The ambassador pointed to this, saying: "Unlike the United States of America, France does not refer to its citizens based on their race, religion or origin."
Mr Noah said the colour-blind approach has not stopped discrimination against African migrants.
"When they are unemployed, when they may commit a crime or when they are considered unsavoury - it is the African immigrants," Mr Noah said.
"When their children go on to provide a World Cup victory to France, we should only refer to them as French."
Mr Noah expanded on the concept, using as an example Malian migrant of Mamoudou Gassama, who was recently given French citizenship after climbing a building to rescue a child dangling from a balcony.
"They said, 'You are now French.' So now I am going, 'Is he now no longer African?'" Mr Noah asked.
Former US President Barack Obama has also waded into the debate about the identity of the French football squad.
During his Nelson Mandela lecture in Johannesburg earlier this week, he pointed to the positive side of immigration: "Just look at the French football team. Not all of those folks looked like Gauls to me, but they are French - they are French."