This image is a tiny one, but the Google recognizes it and offers this larger version:
This appears on a web site called Wikipaintings and attributes it to an artist named Joshua Reynolds. The date of the painting would fit Jean Baptiste Brouillard -- begun 1777 and completed 1778, but it is titled "The Dilettanti Society" (the Wikipedia entry for which I've linked there). According to wikipedia, it was a "society of nobelmen and scholars which sponsors the study of ancient Greek and Roman art, and the creation of new work in the style." It was a London-based group, founded in 1732.
The wikipedia entry notes some "notable" members, none of whom were identified as Jean Baptiste Brouillard and none of whom even appear to be French or French Canadian. An entry at the National Portrait Gallery seems to suggest a list of people who are the subject of the painting, none of whom are Jean Baptiste Brouillard.
Numerous other entries for the Google image search of this image have similar results.
Time to purge those ancestry.com databases and stop suggesting that this image is of or related in any way to Jean Baptiste Brouillard.