Bouteflika, who boarded an Algerian presidential jet in a wheelchair at Le Bourget airport near Paris, was admitted to hospital at the end of April after suffering a mini-stroke.
His plane took off around 1130GMT, the source said.
The health of the Algerian leader has been a source of huge concern in the north African country, where little has been divulged about his condition since he flew to Paris in April.
Last month, Algerian authorities released photos and footage of Bouteflika on state media, showing the 76-year-old in the Paris hospital where he was convalescing.
The pictures were published to dispel rumours circulating in both Algiers and Paris about the president's condition deteriorating.
But 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.
Before Bouteflika's latest illness, supporters within the ruling National Liberation Front (FLN) had made known their desire to see the president seek a fourth term in the election scheduled for next April.
But now there are signs that the succession race has begun, at least unofficially, with several people recently declaring themselves candidates.