From one Ethernet to the other

I think you already know that this will work only if both Ethernet links operate in the same mode, which must be full duplex.

Namely they must be both 100Mb full duplex, or both 10Mb full duplex.

Moreover you must make sure the phy clocks are synchronized, otherwise rx signals coming from one phy would not be sampled correcly into tx ports of the other phy.

You said you don't have a MAC, or you don't want to use it. Anyway you need at least a MDIO interface to configure the PHYs for proper operation.

I'm concerned if DE2-115 pcb implements the required strapping pins, since a MAC with MDIO is supposed to be used inside the fpga.