Jonathan was born in 1713. He passed away in 1785.
Sources
Find A Grave, database and images (https://www.findagrave.com : accessed 01 August 2018), memorial page for Lieut Jonathan French (unknown–13 Sep 1785), Find A Grave: Memorial #82577284, citing Ye Old Cemetery, Danville, Rockingham County, New Hampshire, USA ; Maintained by Linda Mac (contributor 47062703) .
"New Hampshire Death Records, 1654-1947," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FS29-3J5 : 12 December 2014), Jonathan French in entry for Henry French, 30 Sep 1746; citing Kingston, Bureau Vital Records and Health Statistics, Concord; FHL microfilm 1,001,076.
"Pedigree Resource File," database, FamilySearch (https://familysearch.org/ark:/61903/2:2:3Q1T-19X : accessed 1 August 2018), entry for Jonathan /French/, cites sources; "Little Family Tree" file (2:2:2:MMD8-B2R), submitted 18 September 2014 by michaelalvidrez [identity withheld for privacy].
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DNA Connections
It may be possible to confirm family relationships with Jonathan by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Jonathan: