No, you generally cannot find free camping on the California Coast. Free camping can be hard to come by because most coastal lands are part of private property or public parks that charge camping fees. Campers can, however, usually find free camping by heading inland even just a bit to national forests like Los Padres National Forest, which offers free dispersed camping in some areas. In the northern part of the California coast, you can also find some free camping options in Humboldt County's King Range National Conservation Area, such as the Mattole Campground.
Always research any permit requirements, camping, rules, and regulations in advance of arrival, and keep in mind that free camping spots are often primitive with no amenities or facilities. To find cheap camping on the California Coast, consider a service like Hipcamp.