Ok I was able to figure this out I think. Yes we are related through both your Schwoerer and Burgun ancestry.
Pierre was the son of Gaspard Schwoerer and Madeliene Reinberger.
He was born Sept 1, 1765 in Rosteig, Lorraine, France. The 3rd child.
Brother Nicolas born May 14, 1759 in Soucht, Moselle, Lorraine, France.
Another brother, Martin was born around 1761 in St. Louis canton Bitche (pronounced like beach), Moselle, Lorraine France
Also, half-sister Elisabeth born May 10 1776 St. Louis-Bitche, Moselle, Lorraine, France.
He married Marie Madeleine Burgun in 1801.
She was born Oct 24, 1776 in Meisenthal, Moselle, Lorraine, France.
She was the 4th child of Nicolas Burgun and Anne Angelique Maison. She was one of 10 children:
1. BURGUN Joseph Born mar 16 Feb 1773 à Meisenthal (57).
2. BURGUN Marie Madeleine Née le jeu 10 Mar 1774 à Meisenthal (57). Not sure what nee le jue means. I have sent an email to my cousins to find out Nee is short for naissance which is birth.
3. BURGUN Pierre Né le dim 16 April 1775 à Meisenthal (57).
4. BURGUN Marie Madeleine Née le jeu 24 Oct 1776 à Meisenthal (57).
Mariée en 1801 avec SCHWOERER Pierre
5. BURGUN Catherine Née le (p) sam 10 Apr 1779 à Meisenthal (57).
6. BURGUN Adam Né le ven 11 Aug 1780 à Meisenthal (57).
7. BURGUN Georges Né le jeu 25 Oct 1781 à Soucht (57).
8. BURGUN Jean Nicolas Né le mar 16 Dec 1783 à Meisenthal (57).
9. BURGUN Marie Angélique Née en Oct 1785 à Meisenthal (57).
10. BURGUN Appolonie Catherine Née le mar 26 Dec 1786 à Meisenthal (57).
I have info on these lines going back more generations. Do you need that information?