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RR-Net works on top of the MMC Replay cartridge. An older version fits the Retro Replay or MMC64 (but I'm not sure if anyone has ever used it with the latter cartridge).
TFE is a stand-alone Ethernet card for C64.
1541 Ultimate now has an option of integrated Ethernet adapter, but it's very expensive and its main purpose is to be a solid-state replacement for the 1541 drive (which might actually fit your need quite well in itself taking away the need to xfer to real floppies unless you specifically want that).
There are others too, such as Jim Brain's serial project, but that's all the way in America. Of course, you might be too.

You could check the Network section of this forum to find out more or simply Google "C64 Ethernet" or similar for additional information.