The 33-year-old Team Sky rider has denied any wrongdoing and is confident that he will be cleared after an investigation by the sport's governing body Union Cycliste Internationale (UCI).
Team Sky said they were fully focused on the race, which begins on July 7, and would not let Hinault's "uneducated comments" hinder preparations.
"Chris has not had a positive test, rather an adverse analytical finding for a prescribed asthma medication," Team Sky said in a statement on Thursday.
"As an ex-rider himself, Bernard will appreciate the need for fairness for each and every athlete. And at the current time, Chris is entitled to race."
Hinault was quoted by British media as saying: "Christopher Froome should not be at the start of the Tour.
"The peloton should put its feet to the ground and say, if he is starting the race, we won't start.
"Quite simply because he has tested positive, for me this is not an abnormal test. The people at the UCI should have said, you have been caught, so you should not be racing."
Froome, who has won the Tour de France four times, became the first Briton to win the Giro d'Italia in May.
Hinault had earlier said that Froome should not have been allowed to compete in the Giro d'Italia and that the Briton cannot be listed among the sport's greats.
(Reporting by Anirban Paul and Aditi Prakash in Bengaluru; Editing by Andrew Roche)
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