Brussels airport (Zaventem) is connected to Kortrijk by rail, with trains departing every 20-30 minutes. The train station is located in the basement (level -1) of the terminal building itself. You can pay by credit card. The journey takes 1 hour 30 minutes and there are one or two changes according to the timetable. For further information on the timetable, please consult the web page http://www.b-rail.be/ (click on the "timetables" section and enter "Zaventem airport" in the departures slot and "Kortrijk" in the arrivals slot).
From Charleroi airport there is a shuttle bus 30 minutes following every Ryanair arrivals, arriving at Bruxelles Gare du Midi. The journey takes approximately one hour and the one-way ticket, which can be purchased on board the bus, costs 10 euros. For further information, please consult the web page http://www.charleroi-airport.com/.
Trains for Kortrijk depart from the Gare du Midi (every 20-30 minutes). The journey takes around one hour. Some trains are direct, while on others a change is necessary. For further information please consult the web page http://www.b-rail.be/ (click on the "timetables" section and enter "Bruxelles-midi" in the departure slot and "Kortrjk" in the arrivals slot).