Although Sarkozy has not yet officially declared his candidacy, few doubt that he will stand in the forthcoming primary of his Republicans party and the press judged a speech he made in northern France last week to be a key step in his campaign.
"In the years ahead what will be left of France?" he asked a hall that was only half full, although with some 40 MPs in attendance. "That's the first challenge. The greatest. The most fundamental."
The former president called on the French people to "wake up" to defend the national identity in the face of the "abdication of the elites".
A "tyranny of minorities" is "forcing the republic further into retreat each day", he went on, declaring France to be a "Christian country" that must be "respected ... by those who wish to live in it".
Those minorities include demonstrating school students, militant environmentalists, vandals on demonstrations and a "handful of radical Islamists", who left-wing multiculturalists have allowed to dictate that individual rights take precedence over "rules that should hold for all", Sarkozy said.
Then he took a sideswipe at Juppé.
The "new ruling ideology" has infected some on the right, Sarkozy claimed.
"It has struck surreptitiously, singing the sweet melody of 'sensible accomodations'," - a reference to his Juppé's call for dialogue with French Muslims and integration of immigrants rather than the more thorougoing assimilation that Sarkozy has called for.
Juppé calls for respect for diversity
Juppé, a former prime minister who is now mayor of Bordeaux, hit back on Sunday on his blog and on television, calling for "diversity in unity".
"I don't want an identity that is unhappy, fearful, anxious, almost neurotic," he wrote on his blog. "For me identity doesn't mean exclusion or rejection of the other", pointing out that all the French "do not have the same origins, the same skin colour, the same religion or beliefs" and declaring this "a treasure, a strength".
On the TF1 TV channel Juppé declared that there are "two possible attitudes" to Islam in France.
"If one considers that Islam is by definition incompatible, insoluble with the republic, that means civil war," he warned, advocating a "reading of the Koran and a practise of the religion that is compatible with the laws of the republic", including the equality of men and women.
Juppé has spoken out against Sarkozy's calls for extending the ban on the Muslim hijab now in force in schools to universities and banning of halal alternative meals in school canteens.
His earlier calls for tolerance have led to a hate campaign on social media, Juppé said.
"They call me 'Ali Juppé', describe as the Grand Mufti of Bordeaux, they are writing everywhere that I'm spending a fortune of financing a huge mosque in Bordeaux, which doesn't exist and will not exist," he told TF1.
In reality, he has called for changes to some Muslims' behaviour, calling for imams to preach in French and to have degrees in French history and and laws, and wants a special police force to monitor radicalistion in France's prisons.
Setting the tone for presidential debate
The row is a sign that Sarkozy will return to attacking "communitarism" during the Republicans primary and the presidential campaign, as he did in the 2007 and 2012 campaigns, in part inspired by Patrick Buisson, a hard-right journalist who pushed him to bid for National Front votes.
Last week's speech was partly written by Camille Pascal, a contributor to the hard-right magazine Valeurs Actuelles and was hailed by some of his allies as an attempt to engage Juppé on terrain that Sarkozy considers favourable to himself.
Although opinion polls show Juppé the most popular candidate for the presidency among the general public at the moment, he first has to convince the right-wing faithful to adopt him as candidate.
Whoever is chosen will want to attract voters tempted by the National Front in the first round of the presidential election and, according to the polls, could face the far-right party's Marine Le Pen in a second round that is likely to provide evidence of the rejection of the political establishment that has affected much of the world recently.
National Front vice-president Louis Aliot weighed into the debate on Monday, declaring that there is a "problem of accountability between the religion [of Islam] in itself and the republic's laws" and calling on Muslims to "adapt to republican rules".
To read our coverage of last November's Paris attacks, click here