If the front is braided, then it isn't the original. Someone will have replaced it at some point and it won't therefore be as ancient as the rubber rear hose. You could leave it, but why not replace both front and rear with a matching snazzy colour. At least you'll know where you are then and how old your brake lines are.

What always worries me is, if an older bike is still wearing original hoses, it doesn't instill confidence that the fluid has ever been flushed out and changed. Something more important than changing the hoses themselves and should be done every two years. Do you know when your brake fluid was last changed?

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