This site has all the addresses of the EU enforcement authorities
http://apr.europa.eu
Silent Bob Jerkero says you can bring your case in Switzerland, as it is a signatory to the Montreal Convention but you would have to be using the court system as there is no enforcement authority that we know of in Switzerland, but you can check that again locally.
To avoid court costs, we like the remedy of the EU complaint to the enforcement authority in France as the problem occurred on the Washington to Paris leg of your journey and the EU rules apply to flights entering the EU (as well as leaving).
Before filing any case in Switzerland we suggest that you take advice from a Swiss lawyer as to how the 2 year limitation period will be calculated. Is it from the date of the incident or from the date of the refusal of compensation by the airline?
Silent Bob Jerkero thinks US courts will count it from the date of the incident.