The health pass/ le pass sanitaire is being developed for intra-European travelers. The United States has not been part of the implementation. You will be asked for something different to enter the country. You will know before you go what is necessary.
Furthermore, within France le pass sanitaire is for access to large events such as rock concerts, festivals, large theaters, and trade fairs. It is NOT needed for restaurants, museums, tourist sites.
Since we need to ask a question: should you be concerned?
Update: we received a message from the office of the Député who represents French citizens living in North America. He said that the health certificate hasn't even been voted on in the Assemblée Nationale. It has not been approved. He also reassured us that they are working to find a solution for those of us who have been vaccinated outside of France.