South France doesn't sound natural at all and I don't think you'd find many people use it here in the UK. It's either Southern France or (The) South of France. It's a little different to "The Gambia" which is an official name. Just out of curiosity AlexinNotTurkey, is English your mother tongue?
I disagree. I'm from the UK and I would use it without the 'the', although I agree it's more common with it. But it would be completely acceptable to answer the question 'where are you going on holiday' with 'South of France'. The 'the' would only be necessary if you made it a full sentence e.g. 'I'm going to the South of France'. But Güney Fransa is not a sentence, so 'South of France' is fine. Also, South France is just plain wrong and should definitely not be the suggested translation. It's like saying 'United States America'.
Yes, the South of France, where the word south is used as a location, a place, would equal South France.
But if you'd use 'South of France', without the the, that would be the region below France on a map.
My remark was that "the South of France" does not equal "South of France". The Turkish sentence must be translated as the former, 'Le Midi', or South France.
To me, it seems that the use of North, South, East and West indicates a SEPARATE entity: North Korea, South Sudan, East Timor, West Germany.
For areas WITHIN a country or state, we tend to use Northern, Southern, Eastern, Western: Northern California, Southern Italy, Eastern Canada, Western France.
That's why no native speaker in this thread has said that "South France" sounds correct.