I have at least 2 Liquie's/Lecuyer/Cooks that moved to Holyoke MA from Pittsford VT. I am pretty confident that they are brothers. Their father would be Francois. One is John (Jean-Baptiste) and the other is Sandy. Briefly, John and Sandy had sons named Joseph. In fact, most of the family had Jospeh's making a generation of cousins with similar names. Both men also had daughters with similar names: Sandy had a daugher named Ella Jane (ca 1870) and Ellen (ca 1872.)
Both John and Sandy also used the name Cook. Though I think Sandy used it first and as early as 1880. (Census)
Sandy married a woman in Vermont named Alvira or Elvira.
Does any of this sound familiar to what you have uncovered? I can send you more info if needed.