Originally it worked similarly to the OUIGO model (i.e. expanding the market instead of direct competition- competing with itself instead of having the risk of a rival doing so) and 2 conventional TGV Réseau sets underwent an internal refresh. However, the core TGV division took one back and now Izy runs with the remaining set, which is often substituted for a conventional Thalys set.
The services run via Creil, Longueau before joining the LGV near Arras to increase profit margin due to lower track access fees than the full LGV. As Izy is run by Thalys, they “pay” SNCF Réseau for track use.
The trains are still sold as this, longer than conventional Thalys route, but during service disruption and engineering works, the Izy is attached to the next standard Thalys departure and it arrives at roughly the same time. That way customers aren’t entitled to compensation as the delay is less than 60 mins.
There are reports that Izy will imminently require an unrefurbished Eurostar TMST/373 set. If this occurs, the operation will either become slightly more complicated as it would mean there is a mixed Izy fleet or that SNCF could take back the remaining Izy TGV set.
I think this is suicide for Eurostar as if their set proves successful for Izy operations it will give a few people a few ideas about the London route for low-cost high-speed rail which would cannabilise the core Eurostar business. The scrapping of the rest of these sets prevents their procurement by potential competitors, which is a good thing for Eurostar, so I’m not too sure why they would want to go ahead with this set loan/sale.