Not quite: health insurance is not called tax in the US, yet is a benefit under the French system with premiums paid by the employer.

Not quite: An employer in France must provide a private health insurance plan to employees. It is paid out of the pocket of the employee and they can't refuse it.

France has good public health service but it's also pushing private health insurance down the throat of everybody through their employers, quite like the UK or the US. The large majority of the population has double coverage.