Anti-racism groups are calling for French authorities to investigate racist and anti-Semitic graffiti targeting Paris Saint-Germain striker Kylian Mbappe.

SOS Racisme and Sportitude, bodies that combat racism in professional football in France, have requested an investigation be opened into the abusive graffiti found on Paris' rail system aimed at the World Cup winner.

Extremely offensive words and a Celtic cross -- a symbol often used by far-right extremists -- were sprayed in black paint on the RER C, one of the overland-underground lines that crosses the French capital.

"By attacking Kylian Mbappe, this or these individual(s) are deliberately attacking the image of France: a diverse France that they cannot stand," SOS Racisme said in a statement.

"Kylian Mbappe is a symbol of a mixed-race France that succeeds, a fact that is impossible for some people to accept.

"This graffiti constitutes a violent attack on a France that brings us all together. It must absolutely be denounced and punished, because, in addition to being insulting and denigrating, it's a move designed to divide."

Yohann Roszewitch, the former head of SOS Homophobie in France, tweeted the words: "On the RER C or when homophobia, racism and anti-Semitism are now displayed in a totally open manner," to accompany the picture which brought the incident to light.