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Memory Alpha
Real World article
(written from a Production point of view)

François de Picard (Right) and Madame de La Barre (left)

According to background material created for Star Trek Generations, Françoise de Picard was an ancient noble in 16th century France.

He and Madame de La Barre were the founders of the Picard family line, and drawings of them are on the first page of the Picard family album. He was a distant ancestor of Starfleet Captain Jean-Luc Picard. (Star Trek Generations)

This and the family tree in the album imply that they are the farthest back recorded Picard or La Barre known.
The name Francoise (properly spelled Françoise) is actually a female name, the correct male form being François. However, it is unknown whether Francoise was the result of a misunderstanding or was simply a typo.

The article containing this information was included in the Picard family album during the filming of Generations. However, the information is non-canon as the article was never seen on-screen.