FPGA designs are typically synthesized from Verilog or VHDL, which are hardware description languages (HDLs). System C is a very C-like HDL, and there's at least one more C-like HDL whose name escapes me at the moment. A synthesis path from C to hardware is a bit of a holy grail, as it would allow a single design to be realized in hardware or software.
It is also possible to load the FPGA with a microcontroller or microprocessor design, and run typical C code on the synthesized CPU. This allows you to connect custom hardware peripherals to the CPU, or even modify the architecture of the CPU to explore new CPU features.
If you interface the FPGA to external peripherals, you'll probably learn useful things about interfacing, reading datasheets, etc that will apply to microcontroller work.
-j