The Frenchman was stabbed while in bed on Tuesday by a Portuguese man in his 20s who broke into the apartment where the cook was living with his girlfriend, Le Matin reported, citing information it obtained from the village.
The victim tried to flee but was killed by the attacker, while the girlfriend was injured in the hand, the newspaper said.
Valais cantonal police remain tight-lipped about the affair, which they have identified as a homicide.
Officers arrested an “individual” shortly after discovering the man’s lifeless body in an apartment in the village on Tuesday, police said.
Police said they were earlier contacted about a dispute in the apartment.
The individual arrested is in detention while police are seeking information from the public that might shed more light on the incident.
Neither police nor the investigating prosecutor are commenting further.
Le Matin, however, reported that the victim was originally from Bordeaux and had come to Grimentz as a seasonal worker at a restaurant in the village.
He was living in an apartment with his girlfriend, the newspaper reported.
The victim was about to become a father, according to 20 Minutes online, citing information from a resident of Grimentz.
Le Matin said the couple knew the assailant well.
On the afternoon of the incident the three were seen together, the newspaper said, adding that according to its sources the attack was motivated by a dispute over money.