As US and French citizens you are entitled to a 30 day tourist visa exemption on arrival. I believe a visa would have to be applied for in your home country. In my experience there should be no problem at Thai immigration as they don't ask for departure info.

There is a greater likelihood of your carrier refusing boarding if you don't have proof of onward travel within the 30 day period so arrange this before you head to the airport and have it handy at check in.