Blending in while standing out.
Expats love to think of themselves as truly French or Brazilian (or insert nationality of adopted country here). They spend many years working hard on fitting in, on learning the language, and on adapting the mannerisms of the locals. They eat local food, dress like the people in their city, and do their best never to be noticed.
This is problematic for an Expat because they also love to stand out. They enjoy the thrill it gives them to be the exotic one in the room. Remember, the Expat grew up looking and talking like everyone around them and this never got them any attention at parties. Suddenly the Expat has a hook, and standing out is the perfect icebreaker if the Expat wants to make friends (and all Expats do).
These two conflicting Expat desires can cause a lot of anxiety for the Expat. If you should happen upon one, proceed with caution. Approach the Expat slowly and initiate conversation. Even if someone has pointed out the Expat and mentioned the Expat's nationality, it is rude to immediately launch into dialogue in the Expat's language. While many Expats appreciate you can speak their language, they prefer not to be thought of as incapable of speaking yours.
Once you've introduced yourself, ask the Expat about life in your common city. Where do they live? Where do they shop? You may then ask them where they are from. Most Expats love talking about where they come from, even if they seldom identify with their country of origin. You may then turn the conversation back to the city you have in common. Ask them if they like where they are living, and if they've had a chance to travel to surrounding areas.
If you have followed this advice, you have now secured the Expat's good opinion. You are free to maintain a friendship with the Expat.
NB: For Expats who encounter other Expats, the formula is the same except you won't need to proceed with as much caution at first. Expats who encounter other Expats of the same nationality: do not squeal and declare 'ME TOO!' when you find out you hold the same passport. Just because you share a nationality does not mean you have anything else in common.