As others say, you definitely have time, and if it is your brother's only chance, then you definitely should.

One thing to note - you state you are in on a Sunday...

Bad news - this means less and slower trains.
Good news - less traffic
Bad news - most shops will be closed
Excellent news - definitely no Strikes....

One thing you might want to consider when you get to St. Michel/Notre Dame area is jumping in a cab and asking the driver to do a circle trip Notre Dame - Tour Eiffel - Trocadero - Etoile - Champs Elysées - Louvre - Notre Dame.

That way your Brother see a lot of the sights, on a Sunday in January it should only take 30 minutes and cost around €15...

You could add in the Opera on the trip - but you might get stuck in traffic due to the Winter sales around Blvd Haussman