I have found two Madel families in New Orleans in the mid-1800s. Madel is an extremely rare name in the United States. To have two families in early New Orleans not related is not likely.

The two Madel families in New Orleans in the 1850s were:

The first family is Henry and Anna Nagel Madel. Henry was born in 1815 in either Germany or New Orleans.

The second family consisted of a brother and sister, Magdalena (1832) and Henry H. (1831).

There seems to be some simularity in the names of their children.

Henry and Anna Madel had Helena, William Henri, Augusta and Johanns.

Magdalena Madel Langhoff had William and August.

Henry H. Madel had Henry, Helena and William.

Two Madel Families

Henry (Heinrich) and Heinz Madel:

The father of William Henri Madel is Henry (Heinrich) Madel born in Germany in 1815 according to the 1850 U. S. Census for New Orleans. William H. had a sister, Helena Rebecca, born in 1845 in Louisiana.

The passenger list for the ship Leibnitz arriving in New Orleans from Hamburg, Germany on November 2, 1850 listed a Heinz Madel born in 1815 in New Orleans. Both Heinz and Henry were grocers.

Traveling with Heinz on the Leibnitz was Helena Madel born in 1831. Henry also had a daughter named Helena born in 1845 according to the 1850 Census.

Henry and Heinz are most likely the same person. Can't resolve the age difference in Helenas.

George Chavigny Naturalization

George (Jurgen) Bey was a witness to the naturalization of George Chavigny in 1868.

George Chavigny's wife, Helena Rebecca Madel, was the sister of William H. Madel. George Bey married Magdalena Madel Langhoff about 10 years after the naturalization. This indicates that there may have been some relationwhip between the two Madel families in New Orleans in the mid-1800s.

To this point I haven't been able to identify the common relation. 

George Chavigny Naturalization

Michael James Reilly and Margaret Reilly Madel

Based on the Michael James Reilly family research, Michael was the brother of Margaret Reilly, the wife of William Edward Madel. This is the result of research performed in the 1970's and appears to be well founded.

Other supporting items:

Mary Ellen Madel, daughter of William Madel and Margareit Reilly was the sponsor for the baptism of Ann Maria Reilly, the daughter of Michael James Reilly in 1878.

Michael James Reilly and Margaret Reilly Madel both lived on Penrose Avenue in 1880.

Michael James Reilly was released from the Gratiot Street prison in St. Louis after the Civil War and stayed in St. Louis. This could be the reason Margaret and her children moved to St. Louis after her husband, William H. Madel died in 1872 in Jefferson, Texas.

Ann Maria Reilly Baptism

The name of the parents of Michael James and Margaret Reilly Madel:

Father:

Philip - Michael James Death Certificate

James - Margaret Reilly Madel Death Certificate

Mother:

Agnes - Little Sister of the Poor records

Bridget - Margaret Death Certificate (reported by Little Sisters of the Poor)

Alice Smith - Michael's Death Certificate

Mary Smith - Reilly family World Family Tree

There are several possibilites such as Philip James or James Phillip. I don't know who gave the Little Sister the information on the parents and they had a different first name on their records and what they reported for Margaret's death certificate. Because of this I am leaning toward Philip and Mary.