Maybe you were out of school the day they explained that the State of California is one of the 50 "Stars" on the Stars & Stripes, and is therefore part of the Federal Republic of these United States of America, and thus subject to US Federal Law?
California (as a State) cannot "give you rights that are are in conflict with US Federal Law", I'm afraid....unless the Executive Branch choose to ignore such edicts and the Judicial Branch choose not to prosecute them!
There's no need to address it in a state constitution, as it is addressed in the Constitution of the United States, which supersedes all state constitutions.
I read Article 1 (DECLARATION OF RIGHTS) of the constitution of California and couldn't seem to find ANYTHING related to firearms. It's an extremely long article so I quickly read through it looking for key words, but it appears the topic isn't really addressed. I don't know if I just didn't look hard enough or if it really isn't there. I know they have to address it and I figured it would be safe to assume that it would be in the 'DECLARATION OF RIGHTS' article. Maybe not? Please, if you can, inform me.