Arduino doesn't run either C or C++. It runs machine code compiled from either C, C++ or any other language that has a compiler for the Arduino instruction set.
C being a subset of C++, if Arduino can "run" C++ then it can "run" C.
If you don't already know C nor C++, you should probably start with C, just to get used to the whole "pointer" thing. You'll lose all the object inheritance capabilities though.