Again, no. Not sure where you get the "free" imputation, but it is patently untrue.
In America, we have the right to life, liberty, and the pursuit of happiness.
The right to life is not free. The State is not obligated to provide the means of living free of cost or charge. An indigent may be required to work in exchange for benefits, or in the case of unemployment compensation, to work at the task of finding work.
The right to liberty is absolutely not free. Police, soldiers, and others are paid by the State to protect and provide liberty to the general populace. In turn, the People are taxed to pay for the military, the police forces, and the courts.
The pursuit of happiness is likewise not presented as a free enterprise for the citizen. A man may choose to pursue a college degree in Accounting. His education is not provided by the State free of charge, even if he were on scholarship, as the university is subsidized by public funds that in turn come from various taxes and fees. The man graduates and continues his pursuit of a CPA, and may have to pay to take a test to certify and possibly another fee to register and be licensed by the State. He is promised the right to pursue what will make him happy, within certain bounds, and he then must pay to do so.
I have the right to own private property, as opposed to a wholly socialist model, yet I must purchase the property I want. It is my right to own it if I choose, but I do have to pay. It becomes my privilege to own it when exercised but it is a right I have to acquire it.
Free and innate right are not synonyms.