I was puzzled as well by the lack of records for Jean-Baptiste Noreau. Fortunately, since I am French-speaking, I was fortunate enough to piece together various bits of information and get the facts straight.
Here is what I was able to find out:
The one birth date I found for Jean-Baptiste, son of Mathurin Noro (Noreau) and Marie-Josephte Marchet, was May 1st, 1734 in L'Ancienne-Lorette, Quebec. That date is debatable in view of the other information you will find below.
Soon after the British conquest of New France, Jean-Baptiste returned to France. In 1763, in Saint-Malo, he married Anne Francoise Roberte Le Nouvel. That explains why no record whatsoever can be found in Quebec listings.
With his wife and father-in-law Pierre Le Nouvel, he boarded the ship Fort to take part in the French government's plan to set up another New France in Guiana. Indeed, Jean-Baptiste "Noros", from "Kebek" is found in the 1765 census in Sinnamary, Guiana.
A child born to the couple on Aix Island, France, in 1763 died on the voyage and was buried in Sinnamary.
The couple did not remain there long, as they are unlisted in the 1767 census. Somehow, they made their way back to Quebec, probably returning with exiles to Great Britain, where they had a child baptized in 1770.
Jean-Baptiste, a barrel-maker, is listed as a member of the civil militia that found the American troops led by Montgomery that attempted to seize Quebec City on Dec. 31, 1775.
Little is known of him between that time and 1782, when he resurfaces as the father of a child baptized in Chambly. From there, his family moves to Pointe-Olivier/Saint-Mathias up until around 1796, when it finally settles down in Saint-Constant.
Already, around 1796, Jean-Baptiste had his mind made up to live as a French citizen. In 1796, a letter he is the alleged author of was sent to the French consul in New York City asking that the Revolutionary government of France undertake to recapture Quebec.
Another such message is sent to Napoleon in March 1805, with Jean-Baptiste travelling to France to deliver it in person. His son Jean-Baptiste (Jr) travels with him, but he is too sick to travel beyond New York City. Jean-Baptiste arrives in Bordeaux, France, in September of 1805. That is the last that is heard of him.
Apparently, he never returned, which explains why Anne Francoise Le Nouvel (also named Denonville, Desnouelles, and other forms in various records) died alone in L'Acadie in 1821.
I believe that Jean-Baptiste's story would be the basis of a wonderful novel that I am planning to write.
Did I mention that I am the great-grandson of his great-granddaughter Lea Noreau?
Best regards to you and to all extended Noreau family members.