Whether you have to file a California tax return depends on the amount of your income, not how much time you are there. (There's no such thing as "just a visit.") Any income that you earn for working in California is income from a California source, and is subject to California tax. If you have any California source income at all, you have to file a California nonresident tax return if your income is more than a certain amount. And the filing requirement is determined by your income "from all sources," not just from California sources. That's basically the total income on your federal tax return. You can read the details at the following link on the California Franchise Tax Board web site. You probably do have to file a California nonresident tax return.
Do I Have to File?
Since you live in Florida, which does not have a personal income tax, there is no concern about your California income also being taxed by Florida.
A temporary assignment in California will not make you a California resident, even if it's 10 weeks, as long as it is clearly temporary, Florida remains your home, and you intend to return to Florida when the temporary assignment ends.
It doesn't matter where the company that you work for is located. What matters is where you work and where you live.
