Canberra,
Earlier this year I was booking Cardiff to Singapore, Cardiff only being served by KLM, not available directly on KLM or AF websites but available on such sites as
Cheap Flights | Search & Compare Flight Offers - Fly.com , and on price, rather than book on KLM I booked and travelled on AF8348 (operated by KLM) CWL/AMS then I flew with AF AMS/CDG/SIN and with good connection times.
For an airfield, and catchment area, the size of SOU there is little, if any, need for 'KLM Air France' to operate 2 routes!