The Premier League side signed Sala for a club-record fee in January, but the plane carrying the striker went missing over the English channel as he travelled from Nantes to Cardiff to join up with his new team-mates.
Cardiff delayed their initial payment for the Argentine striker as chairman Mehmet Dalman said there were "anomalies" in the deal that need to be investigated beforehand, prompting Nantes to threaten legal action.
"Of course, if we are contractually obliged to pay them then of course we will. We are an honourable club," Dalman said.
"But if we are not - and there are some anomalies in that - then surely you would expect me as the chairman and guardian of this club's interests to look into that and hold our position? That is what we are doing."
The French club then granted an extension on the first deadline, but Cardiff have seemingly held off making that payment.
A statement from FIFA confirmed that Nantes have now taken the case to a higher authority.
"We can confirm that we have received yesterday evening a claim from FC Nantes against Cardiff City in connection with the transfer of Emiliano Sala," the statement read.
“We are looking into the matter and consequently we have no further comments at this stage."
On Monday, Cardiff expressed "grave concerns" over the legality of the flight after an interim report was published by Air Accidents Investigation Branch (AAIB).
"We have grave concerns that questions still remain over the validity of the pilot's licence and rating to undertake such a journey, as identified in the bulletin," a statement from the club read.
"We are also concerned to discover that the trip involved an aircraft which did not conform to either UK CAA or US FAA requirements for commercial activity and therefore may have been operating unlawfully."
Sala's body was recovered from the wreckage two weeks after the aircraft went missing on January 21. The body of the plane's pilot, David Ibbotson, has not been found.