Cape Town International Airport: Pre-book a private transfer or collect a rental car: Franschhoek is about 75 km away and realistically takes 1–1.5 hours, traffic depending. Budget roughly R1,000–R1,800 per vehicle for a private transfer; a shared shuttle can cost less but has limited schedules. There is no rail link and no useful airport-to-Franschhoek public-transport option—do not try to stitch together local minibuses with luggage.
Cape Town city centre: A pre-arranged transfer, rental car or private driver is the sensible move; allow about 1 hr 20 min door to door. The nominal bus-and-taxi combination is not a practical visitor transfer, especially after dark or with bags.
Stellenbosch: Drive, use a booked transfer/taxi, or take a local minibus taxi if you are travelling light and comfortable with informal transport. The R45 is the direct route; allow roughly 35–45 minutes. There is no train service to Franschhoek.