Drinkers reportedly hurled anti-Semitic abuse at the victim, a 21-year-old student at the London School of Economics, and broke his nose on a night out in the Alpine resort of Val d'Isere.
The fight broke out after the student took offense at other members of his group playing a game called "Nazi Ring of Fire", involving cards arranged in the shape of a swastika, several reports said.
"These are disturbing allegations relating to events which took place on a foreign trip organized by the Students' Union," said an LSE spokeswoman.
"Both the SU (Students' Union) and LSE are investigating these events and are prepared to take disciplinary action if the allegations are shown to be true."
Officials will examine a video of the incident, the spokeswoman said.
The assault follows the launch of a probe by French prosecutors into a Nazi-themed British stag party at another Alpine ski resort last month, at which a British lawmaker was present.
Aidan Burley lost his post as a parliamentary aide for attending the party in Val Thorens, around 90 kilometers (56 miles) from Val d'Isere.
Under French law it is a crime to make anti-Semitic statements or exhibit Nazi uniforms or emblems in public, unless required for a film, play or other cultural production.
British fashion designer John Galliano was convicted of anti-Semitism last year for ranting at drinkers in Paris's Jewish quarter, and given a suspended fine of €6,000 ($7,600).
The LSE was forced to admit it officials had made a "chapter of failures" after it accepted a £1.5-million ($2.3-million) gift from a foundation run by Seif al-Islam Gaddafi, the son of late leader Muammar Gaddafi.