Seat reservation TGV to Belgium. SNCF does not list non-French destinations.

You can't "book a train" in the Eurail app. You probably registered it in "My Trip". The terminology is a bit confusing, but you probably only registered this train in the app. 

Please do not activate a travel day (connecting a trip from your trip, to your pass) untill just before travelling.

Anyway, answering your question:

You cannot book seat reservations via the SNCF website. You can via the Belgian railways (link below) You can call them, make the reservation at the counter, or via Eurail (least recommended) 

But, weirdly. For the moment, the trip Lille-Brussels doesn't seem to work on the b-europe websites listed here: https://community.eurail.com/train-connections-reservations-47/how-to-get-reservations-105/index2.html?postid=31362#post31362

A couple of weeks ago it still did. 🤔

When do you want to do this journey? 

Alternatively, you can get to Brussels via regional trains. Take the train to Courtrai/Kortrijk (or Antwerp) in Lille Flandres station. Change in Kortrijk (or Gent-Sint-Pieters if your train goes to Antwerp) to an IC to get to Brussels Midi. Bit slower, but no need for reservations. Connection is usually hourly. 

On weekdays you can also change trains in Mouscron, (first Belgian station of the train coming from Lille-Flandres), and get an IC straight to Brussels. 

Ordinary tickets Brussels-Lille probably will be cheaper than a pass day + reservation cost. Ordinary tickets cost 19 EUR on average. A seat reservation on the TGV already 20 Eur. + cost of a pass day. I would really consider the Alternatives.