It has interested me that there is a jewlery store in Toulouse by the name Rivals. However, I am uncertain of the connection with my family. (That is not to say that there is not a connection, just that I have not established a connection).
With the attached Birth Certificate, I have a fair amount of certainty that my great grandmother.. Rivals did originate from Montauban, and lived in Toulouse when she gave birth to my Grandmother.
Thanks to help from Sondrine on this board (for the attached birth certificate) , I was able to search of Montauban birth records in the years 1850-1870 shows around 4-6 families with the surname Rivals, those families may or may not have been related themselves.