A quick trip to Wikipedia says that the Spanish name was Río del Espíritu Santo, River of the Holy Spirit, and the initial French name was fleuve de l'Immaculée Conception, River of the Immaculate Conception, and later the fleuve Colbert or the rivière Saint-Louis.
> The word Mississippi itself comes from Messipi, the French rendering of the Anishinaabe (Ojibwe or Algonquian) name for the river, Misi-ziibi (Great River). [1]
I guess technically it’s the Anglicized French transliteration of the Algonquian name that stuck. Why that happened has more to do with the French-Indian war.