The G3258 is an Intel socket LGA 1150 CPU while FX 8300 is an AMD socket AM3+ CPU. Yes, a new motherboard would be needed, absolutely incompatible.
If you want to see what works and what will not, use this website (I made an assumption from your name that you are european but the website has other versions such as USA and Canadian).
http://de.pcpartpicker.com/