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I have 13 Jean or Jean-Baptiste Tessiers. Depending on what he did after arriving in the US, I you could probably make some progress first and foremost by finding his Naturalization records. Coming in 1901, he would have been forced to file the long, detailed form if he became a US citizen.
His death certificate, burial records from the Church, and marriage records would also carry major clues...especially if he remained Catholic and joined a French-speaking parish.
I know it's asking a lot, but if you can get back just one or two generations more (to about 1820-1840), you can usually get the entire tree in a day or two. The trick is not to rely on civil records, but to go to Church records, since French Common law made the Catholic Church the official keeper of demographic information. Even after the French left Canada, the Catholic Church continued to keep meticulous records....and most prior to 1850 are very well published. If you can get back there, let us know and we'll do our best to link you back into one of the original Tessier families. Good luck