 Coe was the son of Manuel A. Coe and Mary Caroline Winston Coe.In 1895, he married Anne Chamberlaine of Norfolk, Virginia, who was the sister of Coe's West Point classmate William Chamberlaine.Frank and Anne Coe had one child, William C. Coe, who served in the Army and was the longtime secretary of the Army and Navy Club in Washington, D. C.

After the death of his first wife, Coe married Martha Pratt, daughter Brigadier General Sedgwick Pratt.