The news was reported by the British Broadcasting Corporation.
The French have come up with a new strategy to save the beluga whale.
Rescuers hope that it will help the whale regain its appetite and the energy it needs to return to sea.
Around 70 km north of Paris, the mammal was first seen in the river.
Scientists worry for the animal's health after unsuccessful attempts to get it to swim out.
Rescuers have offered frozen herring and live trout for the whale to eat, but the animal did not seem to have accepted either.
Agence France-Presse quoted her as saying on Saturday that it was very thin and difficult to eat.
Authorities hope that injecting the animal with vitamins will help it get back up the river and out to the English Channel, where it can swim back to its home in the tropics.
The removal of the whale from the river is one of the options being considered, but it would require the mammal to have enough strength to survive.
There were small spots on the whale's skin, but it was not clear if this was a reaction to the fresh water of the River Seine or a sign of the animal's decline.
Scientific observers said the whale was behaving jitteryly, rising to the surface only briefly, and emitting less of the songs expected of a whale.
The whale was far from its natural habitat in the cold waters of thearctic and sub-arctic.
It is rare for Belugas to travel so far from home to feed in the fall. Similar stories aren't uncommon.
The body of a killer whale was found in Normandy in May. The plan to guide the four-metre male orca back to the sea using sound stimuli failed and experts concluded it was seriously ill.
Just a few weeks ago, a whale was seen swimming in the same area. It was thought to have found its way into the river due to a mistake on its part.