1. Other than IRROPS on the day of travel, when it is the operating carrier of the affected flight which handles rerouting, if you book through a TA, it is the TA who must handle the rebooking.

2. If you had purchased the ticket from DL, it would have been DL's responsibility up until the day of travel at which point it becomes AF's responsibility.

Sometimes you will receive a tentative reroute and sometimes not. It does not really matter as you need to either accept the tentative reroute or propose something else.

In this specific case, the distinction between AF and DL is somewhat merged because DL handled customer service for AF in North America and AF handles it for DL in Europe. You nonetheless call the relevant carrier and are transferred based on location.

In this case, the DL agent gave you good information. If the TA had handled any other aspect of your travel, including other tickets, hotels, and the like, having DL take over the ticket might have caused significant problems. As a general matter, best to call the TA and have them handle.