Gerard Filoche, a member of the Socialists' national bureau, also risks exclusion from the party over the Twitter post last Friday night.
It showed Macron with his arms outstretched over the Earth, wearing what appears to be a Nazi armband but with the swastika replaced by a dollar sign.
Behind him are pictures of Patrick Drahi, founder of the French telecoms group Altice; the banker Jacob Rothschild; and the French economist Jacques Attali, as well as American and Israeli flags.
"On the move towards global chaos," the caption reads, a reference to Macron's En Marche ("On the Move") movement that swept him to the presidency earlier this year.
Filoche introduced the image by writing: "A dirty bastard, the French are going to know it," using a phrase that echoes a well-known anti-Semitic slur in French.
The post was quickly deleted, and Filoche told AFP on Saturday that "I've presented my apologies".
"What more do you want?" he added, noting that he was one of the founders of the SOS Racism anti-discrimination association.
The image had already been used in February by Alain Soral, a far-right writer and former member of the National Front party.
Filoche is potentially facing charges of "provoking hatred or violence against a person based on his origins or his ethnic, national, racial or religious affiliation," the source said.
The Socialist Party denounced on Saturday a tweet it called "intolerable, inexcusable and unacceptable" which "tarnishes the basic values of Socialism" and which it considers "a cause for exclusion".
The French-based International League against Racism and Anti-Semitism (Licra) and the CRIF umbrella grouping of French Jewish organisations have said they will file suit against Filoche, as has Attali.