Bulgaria is a member of the European Union (EU) but not a member of the Schengen Area. This means that although Bulgaria uses the euro as its currency, it has its own separate visa requirements. While a Schengen visa is not required to enter Bulgaria, all non-EU nationals, including US citizens, require a Bulgarian visa before traveling to the country.
As long as you have a valid Bulgarian visa, you will be able to transit through Paris airport en route to Bulgaria. This is permitted under "airport transit without a visa," which allows travelers to legally transfer between international flights (i.e., connecting flights) during short layovers without needing a transit visa.