Mullers from France

I am looking for information on a family from France. Alfred Maurice Muller, born around 1845 and died 1906 in NJ. His death certificate says his father was Herman Muller and family stories say his mother was Pauline. We believe that Pauline was married to a Mr. Wyrth at one time, as well.

Maurice married Mary and they lived in northern NJ from about 1870 to his death in 1906, per census records. They had kids: Dana, Maud, Arlington, Charles, etc. He served in the war from about 1861-1864.

Others in the family spelled the last name Mullaire. They lived in NJ and FL. Names Marie, Louise, and Calixte.

Any help would be appreciated!