I would emphasize history, especially those parts we skim over, such as the Dark Ages. Every year of high school needs some history in it. In addition, we need a year of geography.
I would emphasize the trivium more. The last serious grammar unit I was given was in seventh grade. We need to teach grammar, and we need to teach it a lot better than it is usually taught. English grammar needs to be taught from a historical perspective. Literature needs to go back to the canon (which will require re-creating a canon, I know). And we need to get rid of grievance-mongering as a form of literary criticism; we teach youth nothing about what makes the work good or bad by our incessant activism, we only indoctrinate them with the cause du jour.
I would start foreign language instruction much earlier than high school. And instead of just piddling around with cultural bric-a-brac, I would emphasize actual fluency in the target language. By high school, there should be one or two weeks of instruction every year in all subjects in the target language. That means everybody needs to take a foreign language, and everybody needs to be able to do Math, and History, and so on in that language. I would include American Sign Language as an option, as well as Latin.
I would have a Life Skills class (replacing Home Ec and Industrial Tech, perhaps), in which basic budgeting, checkbook balancing, taxation and loans, home repairs, clothing repairs, auto repairs, shopping and cooking were all covered.