My question is how do I trade stocks in other countries that do not have ADRs. I speak French for example, so how would I trade in more obscure French stocks?
Use a broker that gives access to the markets you are interested in. IB for instance is fine to trade french stocks - but is far from offering all world markets.
If you want to trade in anther market, go to the place you want to trade. Find a broker in that market that will give you the best rate, and trade it using these access