Don't change the font - that is what makes it work.
Okay, thank you.
Late reply, I only just saw this 😂 but I'd actually like to disagree with that.
Branding is a core part of forming the personality of the channel to viewers. You wouldn't want BBC Four looking like a childrens TV channel, or a CBBC looking like the BBC News Channel. Just because it might look a little good doesn't mean it's overall suitable.
The logo doesn't look good in certain idents. It might look good in Gallery but it doesn't look good in the dark alleyway. It looks totally out of place and too positive.
Again, if this was actually on TV, I don't think viewers would look at it and get that BBC Four vibe or will take it seriously. I don't have many font suggestions but I'd say you should take a nosy around actual TV channels, similar to BBC Four's category, and see what they'd done. I wouldn't totally rule out handwritey fonts, some may be very suitable, but I think a slightly more serious sans-serif font would be better, or you could take inspiration from ITV Encore.
Other than the font, you need to work on other brand assets and think about how everything would be animated and formed up.