Protesters have accused the groups of deliberate discrimination against Jews and Muslims, who do not eat the meat. They accuse them of handing out free racist soup.
Strasbourg officials have banned the hand-outs and police in Paris have closed soup kitchens in an effort to avert racial tension. The charities have defended offering what they call traditional cuisine to French and European homeless people.
The groups, operating in cities across France and neighbouring Belgium, are not formally linked but are associated with a small far-right organisation called Bloc Identitaire.
Identity Soup, as it has been dubbed by its chefs, was banned in Strasbourg this month after officials ruled it could lead to public disorder.
"Schemes with racial subtexts must be denounced," Strasbourg's mayor Fabienne Keller said.
Although no ban exists in Paris, police have closed soup kitchens in the capital's Montparnasse and Gare de l'Est train stations on administrative grounds. Volunteers were ordered to re-seal soup containers on the basis they did not have the necessary permits to distribute food.
A leading French anti-racism movement has urged Interior Minister Nicolas Sarkozy to ban pork soup give-aways throughout the country.
Bernadette Hatier, vice president of the Movement Against Racism and for Friendship Between Peoples, said the scheme was a ploy to drum up far-right votes ahead of 2007 presidential elections.
Many local authorities have said they are powerless to intervene as the groups are not breaking the law.
National Front spokesman Bruno Gollinisch said that people had the right to be charitable to whomever they want.
He described moves to ban the pork soup kitchens as "revelatory of authorities' alienation from the French people".
Dominique Lescure, head of the Nice-based group Soulidarieta, said pork was a traditional part of French cuisine.
But he admitted wanting to serve the soup to what he called his "compatriots and European homeless people".