We're feeling lucky today. We were looking at previous Mr. Smarty Plants answers on groundcovers for California, and found this previous answer directed to Modesto CA, which is south of you but in about the same climate region. That answer directs you to Las Pilitas Nursery, which has an incredible website on plants for all uses and all native to California. They have much more information on California plants than we do.
We checked into the Trifolium repens (White Dutch Clover), and found this site frorm the Virginia Tech Weed Identification Guide. Apparently, it is considered an invasive weed, in addition to being non-native, having been introduced, probably in contaminated seed, from Europe, North Africa and West Africa. In fact, the "weeds" you are encountering in your garden may very well be grasses native to your area.