My mother always lived in Martinique, but she came to the mainland for medical treatment, where she unfortunately passed away. Is it true that I have one year to file the inheritance declaration with the tax authorities ?

Yes.  Article 642 of the General Tax Code provides that when the deceased has passed away outside the department of Martinique where they were domiciled, the heirs have a one-year period to file the inheritance declaration with the tax authorities (as an exception to the six-month period).