Since "Oui" is French for "yes", that is more probably the origin.
Or, it could just be a meaningless made up word, designed to be something only the French can pronounce!
The "man in sest 61 " has the following description of Ouigo ( https://www.seat61.com/France-trains.htm#iDTGV_trains ):
What is Ouigo?
In 2013, French Railways launched a budget-airline-on-rails called Ouigo, www.ouigo.com. Ouigo trains are totally separate from all other French trains, and can only be booked online at their own website, www.ouigo.com. Unusually, Ouigo's self-print tickets are only emailed to you 3-4 days before travel, and not at the time of booking.
Currently, Ouigo operates several trains a day from Marne la Vallée just outside Paris to Lyon, Aix en Provence, Avignon, Marseille, Nimes & Montpelier using specially-refitted double-decker TGV Duplex trains with just one class of seating, no catering car and no 1st class.
The advantage is ultra-cheap fares from just €10. The disadvantage is that they have applied all the things people dislike about budget airlines to their trains: Departure from a location 45 minutes outside central Paris by RER suburban train, a 30-minute check-in, stringent baggage limits (one item of hand luggage and one bigger bag not exceeding 55x35x25cm) with a €5 extra fee for additional or oversize bags (€40 on board the train if not paid in advance), and no catering.
But if you are determined to reach the South of France from the Paris area for €10-€25 (plus the cost of reaching Marne la Vallée from central Paris and fees for your extra or oversize bags, of course) it may be worth trying. Other travellers may prefer to stick with the regular TGVs or iDTGV, with departures from central Paris, first class available, catering on board, and no baggage size limits...