France's sports minister has accused Nicolas Anelka of a "disgusting anti-Semitic" goal celebration during West Brom's 3-3 draw at West Ham.
Anelka, 34, made the 'quenelle' - described as an inverted Nazi salute.
The French government is trying to ban comedian Dieudonne M'bala M'bala's shows over his use of the gesture.
Dieudonne
Dieudonne's shows may be banned in France
Albion said it was not an anti-Semitic act, but Sport Minister Valerie Fourneyron criticised Anelka, who is also being investigated by the FA.
Fourneyron wrote  : "Anelka's gesture is a shocking provocation, disgusting. There's no place for anti-Semitism on the football field."
But Anelka defended his action, saying:  "This gesture was a special dedication to my friend Dieudonne."
Albion caretaker manager Keith Downing said Anelka was "totally surprised" by the furore, despite the French government announcing on Friday that it was studying legal options to ban performances by Dieudonne.
"It has got nothing to do with what is being said," Downing said. "It is absolute rubbish."
Jewish groups had complained to French president Francois Hollande about Dieudonne's trademark gesture, which they described as a "Nazi salute in reverse". They linked it to increasing anti-Semitic remarks and acts in France.
In return Dieudonne has threatened to sue the groups for calling it a Nazi salute. He calls it "la quenelle" - a word for a fish dumpling - and says it stands for his anti-Zionist and anti-establishment views, rather than anti-Semitism.
Anti-discrimination body Kick It Out said it was in contact with partners in England and France over the Anelka incident and offered support to the Football Association in its inquiries.
Former France international Anelka scored his first two goals for the club in Saturday's draw with the Hammers. He had not played since the 4-1 defeat by former club Liverpool on 26 October.