Houllier, who managed Liverpool from 1998 to 2004, won six major trophies as manager of the Anfield side, which included a League Cup, FA Cup and UEFA Cup success in 2001.
The Frenchman managed his national side from 1992-93, but left after failing to qualify for the 1994 World Cup.
Houllier had a long history of heart problems, dating back to when he was rushed to hospital at half time of a Premier League game between Liverpool and Leeds United in 2001.
We are mourning the passing of our treble-winning manager, Gerard Houllier.— Liverpool FC (@LFC) December 14, 2020
The thoughts of everyone at Liverpool Football Club are with Gerard's family and many friends.
Rest in peace, Gerard Houllier 1947-2020. pic.twitter.com/isHGXIfe5E
A Liverpool statement read: "Liverpool FC is mourning the passing of former manager Gerard Houllier, aged 73.
"The Frenchman was in charge of the Reds for six seasons, leading his team to an historic and unforgettable treble of League Cup, FA Cup and UEFA Cup in 2000-01 and returning the club to the Champions League.
"Houllier -- who recovered from life-saving heart surgery during the 2001-02 campaign to return to the dugout -- later guided Liverpool to a second League Cup triumph of his tenure in 2003 and departed the following year having overseen 307 matches and successfully re-established the club as a modern force.
"Everybody at the club is deeply saddened by the loss of Gerard and our thoughts are with his family and friends."
Houllier's former club Lens also tweeted: "It is with sadness that we learn about the passing of Gerard Houllier, the former Lens manager from 1982 to 1985, and former France boss.
"Our thoughts are with his family and his friends."
Former Manchester United manager Sir Alex Ferguson released a statement on the club's statement: "The news has come as a total shock this morning. Gerard Houllier was still a young man at the age of 73.
"Gerard became a really good friend during his time at Liverpool. We remained great friends after he left and he was always a great ally to have.
"He had fantastic football knowledge which he gained during his extensive and varied career. When we saw each other at UEFA meetings or other events, we would often enjoy a chat, he was always great company and I will miss him dearly. He was a true gentleman.
"It is a sad day for the football world and my thoughts are with his family at this desperately sad time."
Former Liverpool striker Michael Owen, who won the Ballon d'Or in 2001 under Houllier, wrote on Twitter: "Absolutely heartbroken to hear that my old boss, Gerard Houllier, has sadly passed away. A great manager and a genuinely caring man."
Liverpool legend Jamie Carragher also posted on Twitter: "Absolutely devastated by the news about Gerard Houllier, I was in touch with him only last month to arrange him coming to Liverpool.
"Loved that man to bits, he changed me as a person & as a player & got @LFC back winning trophies. RIP Boss."
French champions PSG posted on social media: "It is with great sadness that PSG has learned about the death of our former manager Gerard Houllier.
"PSG sends its most sincere condolences to his family and friends."