Whether or not you paid European VAT on the goods is irrelevant. The US does not care whether you shopped tax free. The important fact is that you are importing the goods into the United States.
You are entitled to an exemption from US import duty, typically $800/person, but see that article for all the details, as there are some cavaets. When you come back to the US, you'll need to declare your purchases on your customs form. If you've exceeded the limit, you may be charged duty (flat rate of 3% on the next $1,000, then the regular rates apply). In some cases, they may wave you through anyway rather than collect a couple of dollars, but this is up to them. Always declare your purchases accurately (save receipts) and the CBP staff will assist you.
It is possible that you owe "Use Tax" (essentially, sales tax that isn't collected at the time of purchase) to the State of California. This isn't unique to traveling abroad; technically you could owe it if you bought something taxable in, say, Nevada and brought it home for your use in California. This would be reported on your annual California state tax return, and you can discuss it with a tax professional. You don't have to pay use tax on foreign purchases that fall into the $800 duty-free exemption, however. If you exceed your CBP duty-free allowance, you might also receive a bill from the state for the use tax owed (the rate is equal to the sales tax as if you bought the items at home).
The US Government's "Know Before You Go" website has useful information for you as well.