Carter to take legal action
Carter, fellow All Black Joe Rokocoko and Argentinian wing Juan Imhoff were the target of an investigation by the medical commission of the French Rugby Federation after testing positive for corticosteroids following last season's domestic Top 14 Final.
But the trio, as well as Racing's medical staff, were all cleared of any wrongdoing.
The club said in a statement that media reports had "blurred public perceptions of their players".
The statement added that they and the players had decided to take action "in order to shine light on how their medical confidentiality was breached."
"After totally justified medical treatment dispensed conforming to the rules, three Racing players saw their medical confidentiality breached when details were reported by the media," Racing added.
"This serious and evident violation must not create any future difficulty for anyone wishing to work securely and transparently with the relevant anti-doping institutions."
Corticosteroids can be used to combat pain, inflammation or allergies.
They can be taken legally or illegally, depending on the method of ingestion.
It is illegal to take corticosteroids orally or have them injected in either the blood or muscle, but they can be injected into joints or inhaled.
Even if taken in a banned manner, athletes can gain permission to do so by applying for the controversial Therapeutic Use Exemption (TUE).
French sports daily L'Equipe originally revealed the positive tests on October 7.
French television channel Canal+ claimed Carter's corticosteroid readings showed 81 nanogrammes per millilitre, with 49 for Rokocoko and 31 for Imhoff, while the World Anti-Doping Agency (WADA) has set a limit of 30.
Agence France-Presse
