Yes, there are direct trains but I would not trust voyages-sncf.com to book train journeys entirely outside France (or for anything else actually). The official site from the Belgian State Railways will show you all the trains and should allow you to buy a ticket online.
Another option to book the tickets would be loco2 (I find the site nicer and easier to use than either SNCF or NMBS/SNCB but they only offer postal tickets for this journey so that's not very convenient).
Finally, you can buy a ticket on the day of travel, at the airport. Apart from international services (especially Thalys) and unlike in France, Germany or the UK, there is no advance booking discounts or seat reservations on trains in Belgium so little downside to buying the tickets at the last minute, except the need to plan some time for it. Besides, your train is little more than a suburban train, Belgium is quite small and Antwerpen is a bit over 30 min away from the airport.
Note that, depending on the site/language, the airport station is also called “Bruxelles Nat. Aéroport” or “Brussel Nationaal Luchthaven”.