A nit: C is _not_ interpreted by the CPU directly. A C program is compiled to machine code. It is this code that is fetched by the CPU during execution.
On Intel CPU's, each instruction triggers a subroutine stored in the CPU and written in microcode. On other architectures (the 6502 comes right to mind), the instruction is directly executed by hardware (apply a pattern to the chip inputs, read the answer from the outputs). The first case could be considered 'interpretation' (but of a machine language rather than C), but the second is not. Applying the word 'interpret' to a transistor changing state would stretch the definition beyond all recognition.