If I am employed remotely by a US company. Do I need a special visa to go to France for a 1 month vacation? If I plan to continue working for my US company, Would this be allowed with a general tourist visa?
Do I need a special visa to go to France for a 1 month vacation?
It depends on your citizenship. Working for a US company or being a US resident is irrelevant. If you are a US citizen, you do not require a visa to visit France for one month, no matter the purpose. You would enter under the visa-free short-stay regime defined in the Schengen Borders code.
If I plan to continue working for my US company, Would this be allowed with a general tourist visa?
For a short stay, there is no distinction between a tourist visa and other types of stays, there is only one type of visas (for those who require one). People who need a visa and come to work for a short time in France also get a generic Schengen short-stay visa.
The catch is that you also need an autorisation de travail beside the visa/right to stay (or, in fact, before applying for the visa). Realistically, you can only obtain that when working for a French employer and it comes with many obligations (contributing to the French health insurance and retirement pension system, complying with French labour law — including working time, mandatory leave, etc.) There is no blanket exception for remote workers.