The French Culture Ministry said the country had lost a "timeless Francophone icon".
Local media reported she had been found dead at her home, citing people close to her. Birkin had a mild stroke in 2021 after suffering heart problems in previous years.
Birkin was best known overseas for her 1969 hit in which she and her then-lover, the late French singer and songwriter Serge Gainsbourg, sang the sexually explicit "Je t'aime...moi non plus".
She had lived in her adopted France since the late 1960s and apart from her singing and roles in dozens of films, she was a popular figure for her warm nature, stalwart fight for women's and LGBT rights.
The "most Parisian of the English has left us," said Paris Mayor Anne Hidalgo.Â
"We will never forget her songs, her laughs and her incomparable accent which always accompanied us."
Jane Mallory Birkin was born in London in December 1946, daughter of British actress Judy Campbell and Royal Navy commander David Birkin.
She first took to the stage aged 17 and went on to appear in the 1965 musical Passion Flower Hotel by conductor and composer John Barry, whom she married shortly after. The marriage ended in the late 1960s.
Before venturing across the Channel aged 22, she achieved notoriety in the controversial 1966 Michelangelo Antonioni film Blow-Up, appearing naked in a threesome sex scene.
But it was in France that she truly shot to fame, as much for her love affair with tormented national star Gainsbourg, as for her tomboyish style and endearing British accent when speaking French, which some said she cultivated deliberately.
Following the break up of that relationship in 1981, she continued her career as a singer and actress, appearing on stage and releasing albums such as Baby Alone in Babylone in 1983, and Amour des Feintes in 1990, both with words and music by Gainsbourg.
She wrote her own album Arabesque in 2002, and in 2009 released a collection of live recordings, Jane at the Palace.
"It's unimaginable to live in a world without you," said French singer Etienne Daho, who produced and composed Birkin's last album in 2020.
It was on the set of the film Slogan in 1969 that Birkin first met Gainsbourg, who was recovering from a break-up with Brigitte Bardot, and the two quickly began a love affair that captivated the nation.
That same year they released Je T'Aime... Moi Non Plus (I Love You... Me Neither), a song about physical love originally written for Bardot in which Gainsbourg's explicit lyrics are punctuated with breathy moans and cries from Birkin.
The song was banned by the BBC and condemned by the Vatican.
Gainsbourg's drinking eventually got the better of the relationship, and Birkin left him in 1981 to live with film director Jacques Doillon. However she remained close to the troubled singer until his death in March 1991.
It was around this time that she inspired the famous Birkin bag by French luxury house Hermes, after chief executive Jean-Louis Dumas saw her struggling with her straw bag on a flight to London, spilling the contents over the floor.
She is survived by two daughters the singer and actress Charlotte, born in 1971, and Lou Doillon, also an actress, born in 1982. She also had a daughter, Kate, who was born in 1967 and died in 2013.
12°C