Two French soldiers and 17 insurgents died in the effort to free Denis Allex who has been held hostage by al-Shabaab for three years, Shabelle Media Network reported.
The execution threat was made in a statement posted on the group's Twitter account.
"After the botched rescue to snatch Denis that attempt by France sentenced Denis to death," the group wrote.
The al-Qaida affiliate said its decision comes after what it called "exhaustive attempts at talks" over his release, euronews.net reported.
The group posted a video in October of a gaunt-looking Allex pleading with President President Francois Hollande to negotiate his release and save his life.