The farthest back we can go (reliably) right now is to Matthieu Garrigues of Languedoc and his wife Susanne Rochet. Anyone claiming to go back further is most likely perpetuating some bad information that has been going around since the early 1900's. You are wise to question and ensure documentation.
Even the Matthieu Garrigues and Susanne Rochet claim is somewhat of a leap of analytic faith as there is no specific record showing that they migrated to the British Colonies. We know that the immigrant ancestors were Matthieu and Susanne but bona fide proof that they are the same couple in Walloon records of the Hague is non-existent right now. Susanne's maiden name is not listed in early records in Philadelphia. However, the circumstantial evidence is pretty darn strong based on their son François (aka Francis). It's a leap of faith in which I feel pretty confident.
Be especially wary of the version propagating that claims to trace the ancestry back to Guillaume de la Garrigues in the 1100's or so.
Matthieu and Susanne Garrigues came to the British colonies sometime between 1713-1714. What makes this all the more interesting is that they first came to St. Christopher and spent several years there. They appear in the census of 1708/9 and military records for their son Matthew Jr. show that he was born on St. Christopher in 1712. Their next son would be born in Philadelphia in 1715.
Most have looked at this St. Christopher connection as the "smoking gun" connecting the family of Matthieu Garrigues and the family Lagarrigue (aka Laguarrigue) that had been on St. Christopher for several decades and then fled to Martinique by the time Matthieu and his family had arrived. What most people may not have considered is that Barbados and St. Christopher were common stops enroute to the Americas as the trade winds and currents that brought the Europeans here led directly to the Antilles. In the days of sail most everyone coming west stopped in or past St. Christopher. There was also a family by the name Garrigues in the Kingston, Jamaica area. This family appears to have come from England and later migrated to Australia. Information on their branch is listed on my site in the "Documented Lineages Project".
Insofar as anything is "proven" in genealogy I believe strongly that the two families are NOT connected and I explain my analysis on my website . Look under the "Myths & Legends" section. At the very least nobody has gotten the connection correct and certainly nobody is offering documentation or evidence. I have also included a genealogy of the Lagarrigue family from one of the French Armorials on my site. You'll probably find that the version you were sent differs from the armorial account of the family.
I'd be interested to see what you may have gotten and I am always interested in any documentation that might prove me wrong. Would you mind sharing with me? I'd also love to learn more about your connections to the Garrigus family.