The CAPM model is based on the relationship existing between an asset and its benchmark market; assuming that the bitcoin could be thought as a currency, according to me, you should take the mean of returns over all the currencies traded and then regress the BTCUSD on the the average currency market returns.
Indeed, although the EURUSD is one of the most liquid and traded currencies, in my humble opinion, it should not be considered as a benchmark of the currency market. Anyway, in this case too you are only approximating the market portfolio, as Roll (1977) suggests.
Maybe you could find pretty interesting the Roll's critique about constructing a market portfolio and testing the CAPM model; here below you can find the paper citation:
Roll, Richard (March 1977), "A critique of the asset pricing theory's
tests Part I: On past and potential testability of the theory",
Journal of Financial Economics 4 (2): 129–176
Hope this will help.