Alejo (Alejandrino) Cabot y Liquet was the one born in France based on US Census Records. Luciano was his son and my Grandfather. From my research, it appears as if Luciano was married twice. If true, my mother, Esperanza, was born of the second marriage between Luciano and his cousin, Adela Ramirez Liquet, my Grandmother. You must be from his first marriage where he was widowed.
I found a marriage registered between a Thais (or Ulais) Liquet to Louis Prosper Capet (or Cabot) on 27 August 1853 in Seine, Paris, France. I do not know if they were the parents of Alejo. By the way, my research shows that Alejo had 2 residences, one in Aguadilla, PR and another in Mayaguez, PR.
There were a lot of Liquet's in the Brittany region of France during the late 1700's and early 1800's.
I am still researching and will let you know whatever I find out, after all, we are cousins!