Can I replace Atmega8 with Atmega328 in my freeduino board?
Shouldn't be a problem. Some later versions already have a ATMega168 instead of the ATMega8. All three are pin-compatible.

In the arduino IDE you should however select a different board (one with a 328, like the UNO). That way the compiler knows the target MCU is the 328, and not the 8.