No, your 401k plan - as a participant - is NOT free. You do pay costs, either directly or indirectly.
Sometimes, these costs are in the disclosures. One important document is the Summary Plan Description. This outlines how the plan operates, whether loans are allowed, what rules govern withdrawals, and sometimes outlines the costs.
Many people, upon seeing this, are surprised to learn that it's not "free".
This article does a good job of highlighting some common fees in 401k plans.
To paraphrase a popular commercial - what's in your plan?