Free software is software which allows its user to inspect its source code, modify it, repurpose it and/or redistribute it. Free software also makes no attempt to dictate how the software is to be used, thus the user may use it as they see fit, even in commercial environment. Some free software also contains share-alike clauses, which require any additions to the software to also be licensed under the same or compatible license, which is commonly referred to as copyleft. Free software is conceptually similar to Open Source software, but it is not the same.
Ability to inspect the software's source code is a major boon for privacy as an independent expert can independently verify that the software does what it says on the tin. You no longer have to take developer's claims on blind faith; you can take meaningful steps to verify developer's claims regarding privacy and security of the software yourself, or you can rely on unaffiliated experts and community at large to sound the alarm if your software contains an anti-feature.
Thus, free software is a gold standard when it comes to preserving your own privacy. With virtually no exception, if privacy is important to you you should almost always opt for free software over proprietary software.
It should always be remembered that free software does not automatically mean that the software is privacy respecting or unhackable. However because the code is so open to feedback and even modification, the odds of it being safer and more private are significantly improved.