This question involves various different interrelated aspects. In particular; employment and business law and taxation, residence requirements and personal taxation. In summary, you can move to Monaco subject to normal residence requirements, and there would be no personal income tax in Monaco. However, if you are a French national, you will still be subject to French income taxes due to the agreements between Monaco and France. With respect to the business side of things, any commercial or professional activity in Monaco is subject to a business authorisation. You could set up a business in Monaco, as a sole trader or in corporate form, or your employer could apply to set up a business there. However, you should note that businesses may be subject to corporation tax in Monaco (at a similar level to France), and it would be wise to review the business activity with a view to optimising taxation.
