Assuming this is a modern turntable with RIAA eq built in, and speakers are self-powered, it really doesn't matter that the colors don't match. One is for left channel, the other the right channel.
Black-and-red speaker connection means this is dump (non-powered) speaker. You need a stereo amplifier with turntable support (PHONO input) between the turntable and the speakers.
And as @jsmithepa mentioned, you have to check whether your turntable has built-in RIAA correction.