The 76-year-old's latest absence has sparked major concern in Algeria given his central role in running the country, and has also generated intense discussion about next year's elections now that it appears unlikely he will seek a fourth term.
Bouteflika, who boarded an Algerian presidential jet in a wheelchair at Le Bourget airport near Paris, was admitted to hospital on April 27 after suffering a mini-stroke.
His plane took off around 1700 IST, an airport source said.
Calls have grown in the Algerian media for the constitution's rarely mentioned Article 88 to be invoked, according to which power temporarily transfers to the Senate leader if the president is incapacitated.
In an effort to dispel rumours that his condition was deteriorating, Algerian authorities last month released photos and footage of Bouteflika on state media, showing him convalescing in the Paris hospital.
The footage showed him sitting in an armchair drinking coffee as he conferred with Prime Minister Abdelmalek Sellal and army chief Ahmed Gaid Salah, who visited him in hospital.
As such, they failed to convince media in Algeria, with many newspapers commenting about his weak health.
After a stint in the famous Val-de-Grace hospital, where many statesmen have been treated, Bouteflika was transferred to the Invalides National Institution, a military hospital in central Paris.
This is not the first time the ageing president has had health problems. In 2005, he had surgery in Paris for a bleeding stomach ulcer and spent a long period convalescing.
A leaked US diplomatic cable in 2007 suggested he might be suffering from terminal stomach cancer, and since being re-elected for a third term in 2009 he has rarely appeared in public or travelled outside the capital.
But now there are signs that the succession race has begun, at least unofficially, with several people recently declaring themselves candidates.
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