It's written in Railteam terms
What is Railteam? What are the quality guarantees of this alliance? Find out more about Railteam services here.
www.eurostar.com
Ideally, you would get your ticket stamped with the special HOTNAT (hop on the next available train) stamp directly from the train manager in the TGV (they are usually located in one of the 1st class coaches, near to the cafe car, but you can usually ask the bar attendant for them if you don't find them) by explaining you will miss your Eurostar connexion, but I doubt most train managers on this route hold it. But you should try it either way.
Since e-tickets are the norm now, I'm pretty sure you won't have any issue with taking a picture of the (green) arrival boards mentioning the train number and the delay or a screenshot of the SNCF connect app showing the delay
You can access the arrival board of any station on the SNCF Connect app home screen and at
https://www.garesetconnexions.sncf/fr/gares-services