The ex-Manchester United player, known to English fans as King Eric, has written to French mayors seeking the 500 signatures from elected officials that are necessary for a presidential bid, Liberation said in a front-page report.
But in an editorial, the newspaper said Cantona was applying one of his legendary footballing feints on the political field, using the unlikely presidential run to secure his real aim – help for the poorly housed.
In his letter to city mayors dated January 4, Cantona did not mention whether he saw himself as a potential candidate for president.
But the 45-year-old said he was "a citizen very much aware of our times", which he argued offer "too-limited chances" to the young and generate "violent" and "systematic" injustices.
He said he felt obliged to speak up "at a time when our country faces difficult choices" and that the current economic uncertainty gave him "a sense of my responsibility".
He added that getting the 500 mayors to sign up to his message on housing and poverty "would allow me to send a simple but clear message; a message of truth and respect".
Speaking to Liberation, Cantona said he "chose the housing issue as it seems to me to be essential and concerns tens of millions of people".
"I had to act at a time when I was likely to be heard."
The presidential election will get under way in April.
As a player Cantona was known for both his genius and ill-discipline, as well as his often colourful and incomprehensible remarks.
Late in 2010 he entered the political and economic fray, calling on his compatriots to withdraw cash en masse as a way to bring banking to its knees – although it emerged that his actress wife had appeared in a TV bank advert.
French and European politicians and bankers condemned Cantona as irresponsible, naive and misguided, and his call to action was not taken up.
Considered one of the greats of the game, Cantona retired from professional football in 1997 and has since turned to acting, notably in director Ken Loach's "Looking For Eric".