Your Realtek PCIe FE Family Controller is probably a 10/100 network device, that means it's max throughput is 100 mb/sec.
The letters FE in the model name stands for "Fast Ethernet" which is 10/100 mb/sec.
In that case, you need a network card which has a specification of 10/100/1000 mb/sec (or Gigabit)
https://www.reddit.com/r/techsupport/comments/2tym6t/can_only_get_100mbps_through_my_lan_its_not_the/