Update 5.50pm: Julien Ruas, a deputy mayor of Marseille, said that the lifeboat fell 10 metres or so from the fifth deck of the Harmony of the Seas into the sea with the five crew members aboard.
He identified the dead crew member as a 42-year-old Filipino. Circumstances of the accident are still unclear.
Local naval firefighters told the AP one person died, two were seriously injured and two were more lightly injured.
The Miami-based Royal Caribbean cruise line said in a statement that the incident happened while the ship was docked in the port of the Mediterranean city.
Update 3.10pm: Royal Caribbean has confirmed that a crew member has died during a lifeboat drill being conducted on the Harmony of the Seas cruise ship in Marseille, France.
The Miami-based cruise line made the announcement on its official Twitter page.
According to tweets, four other crew members received medical treatment following the incident on the Harmony of the Seas.
According to Royal Caribbean's website, the ship arrived in Europe in May and makes stops in France, Italy and Spain.
A statement issued by the company read: "We are sorry to share the sad news that a crew member aboard Harmony of the Seas has died of injuries suffered during a lifeboat drill conducted while docked at the port of Marseille, France.
"Four other crew members received medical treatment in the same incident. We are keeping our colleagues and their families in our thoughts and prayers."
Earlier: One person has died and four others have been injured after a lifeboat became detached from the world's largest cruise ship.
The Harmony of the Seas was docked in the French port of Marseille when it happened.
Two people are said to be in a life-threatening condition.
"One person is dead and four are injured, including two whose lives are in danger," said a spokesman for the fire service.
All five were reportedly in the lifeboat when it "became detached", he added.
It is being reported that the crew were taking part in a safety exercise when the lifeboat became detached from the fifth deck.
The ship - dubbed "Europe's biggest hotel" - cost $1bn and has the capacity to carry 6,780 passengers and 2,100 crew members.
It has been compared to a floating city with more than 2,747 staterooms, 20 restaurants, 23 swimming pools and a park with more than 10,000 plants and 50 trees.
It also boasts what it describes as seven neighbourhoods which include a cinema, promenade, sports and youth zones, an entertainment palace and spa and fitness centre.
At 362 metres long, the 16-deck ship is bigger than the Eiffel Tower and is the widest cruise ship ever built at 65 metres.