It is not easy to establish an origin and even less to find an exact date about when and why the name Falquez was started to use, in its origins FALQUES.. I will try to outline some hypothesis which in the end are just that: hypothesis.
"El Diccionario de la Real Academia Española" (the Royal Academy Dictionary of Spain) defines surname as the family name through which people distinguish themselves and this definition could not be more exact. Actually, it is a family name and therefore it is not a surname at least originally the word that comes together with the first name of a person whether it be motivated for a physical or moral trait, whether it be for a job, dignity of geographical origin as long as this was applicable only to the individual and not to his family. That is, that the surname will be, when it serves for naming the members of a family, that possess or not that original physical trait, work or not in that specific job or are from such and such place that served for baptism. In this case, we could suppose that etymologically Falques comes from FALCO, falcon (hawk). That is, the descendants of the hawking business, in the falconry, could be called the FALCO-EZ. Lets remember that the particle ibn, used by the Arabs to signify "son of", was replaced in Castilla (Spain) for the Z, added to the patronymic. For example: Rodriguez son of Rodrigo; Gonzalez son of Gonzalo, etc.
In "Génesis y Evolución Histórica del Apellido en España" (Genesis and Historic Evolution of the Surname in Spain), by Jaime Salazar y Acha, he writes: "Regarding the change of surnames I do not want to miss quoting here the case of the translations, even though in Spain there were not as numerous. When a person passed from one reign to another, from those that composed the Spanish monarchy, they used to translate their surname. There was no difficulty in understanding that the Centelles in Valencia were the same Centellas in Castilla, the Cervelló, Cervellón, the portuguese Alencastre, Láncaster and the roman Orsini, Ursinos, because in truth it is just a matter of slightly variations in the spelling. But perhaps almost nobody that listens to me would know that FALCO, was in its origin Basque, before passing to Valencia, BELAOCHAGA, since both words mean in their respective languages the same thing, that is falcon."
In sum we could say that around the X century, the Belaochaga Basque, is translated in Falco Catalan and that in Cataluña the patronymic Falques is complemented. Etymologically, according to Francesc de B. Moll in his work "Els Llinatges Catalans", Falques is probably derived from the Catalan word "falca" (wedge, in spanish): "falquer", which its definition is "el qui fa falques". It is equally used in jargon the formations of Castellers, the ancestral technique of the formation of human pyramids.