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The best option is to buy a "Trampoline" ticket on Lille - Kortrijk. This ticket costs 8 Euro and is valid the whole day on all trains (both ways) on the Lille - Kortrijk route. http://telechargement.ter-sncf.com/Images/Nord_Pas_De_Calais/Tridion/flyer_trampoline_occasionnel05_tcm-26-64218.pdf You can buy this at the ticket office, or from the ticket vending machines.
Trying to do it all using "local" transport will make the trip a lot longer, and will unlikely be cheaper than the 8 euro Trampoline ticket.
On weekends SNCF also offers Trampoline tickets to other destinations in Belgium. They're a bit more expensive, but still good deals.