The 48-year-old has been released from police custody in relation to the killings but is still being investigated over his alleged involvement in arms trafficking.
Saad al-Hilli and his wife Ikbal, from Claygate in Surrey, and her mother Suhaila al-Allaf were shot dead on a remote road in Chevaline, near Annecy, on September 5, 2012. A local cyclist, Sylvain Mollier, was also murdered.
French police arrested a 48-year-old, believed to be a former policeman from the Haute-Savoie region of France, in connection with the killings on Tuesday.
Prosecutor Eric Maillaud said he was released after investigators found "no direct link" between him and the deaths. He said the investigation into the murders was continuing.
But he added: "The man will be taken into custody in connection with illicit trading in wartime weapons and ammunition found during searches by investigators."