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Can't you rent a car and drive yourself to your destination ? is it a round-trip the same day or multi-day service?
You could rent a "voiture de tourisme avec chauffeur" (VTC) (similar to a limousine service) to drive you there.
I believe for such an unusual destination ( at least from Toulouse), you'd better get direct quotes from taxi and VTC services.
A quick search would set you back at least 300 euros one-way, if not more. (about the same thing for Uber)
for example :