Commenting on Russian tennis player Maria Sharapova's positive test on Tuesday, Bachelot, a minister under Nicolas Sarkozy in 2007-2010 who has a daily slot on a talkshow on D8 television, said Nadal's "famous injury" was "certainly due to a positive control".
"When you see a tennis player stopping for months it's because there's been a positive control," she said, adding the wish that Sharapova's admission that she had tested positive would open "a new era of transparency in a magnificent sport".
Nadal himself responded on Wednesday, saying he was "beginning to get tired" of such accusations and claiming to be "completely clean".
On Friday his uncle and trainer joined the fray with no holds barred.
"Nowadays, instead of someone's guilt having to be proved, you have to prove your innocence," he told Catalan radio station Rac1. "So an imbecile like this can say whatever horror they like and see what happens."
Toni Nadal said that he was considering legal action.
The Spanish Olympic committee on Friday called the accusation "baseless" and said Nadal had "undergone countless antidoping tests, always successfully".
The International Tennis Federation called Bachelot's statement "not only surprising but also false".
"The names of all players found guilty of violating the tennis antidoping programme are made public," it said.
The comments have aroused indignation in the Spanish media, with the online daily El Espanol referring to the "continuous attacks by France on Spanish sport, always without proof".
Le Monde newspaper has raised Spanish hackles on at least two occasions, when a journalist linked basketballer Pau Gasol's name with that of a doctor named in a doping scandal and when tennis player Yannick Noah referred to Spanish sports players "magic potion".
The Guignols satirical puppet show won notoriety across the Pyrenees with a sketch that implied widespread doping in Spanish sport.
Bachelot herself was not backing down on Friday, telling Le Monde that she was only "repeating comments that are widespread in the tennis world and the press".