I suppose that if you want to be taken for a businessperson, then dress as a businessperson would in a large US city: dark suit (preferably tailored), crisply-pressed shirt, and a Christian Lacroix tie if you're a man, something analogous for a woman.
If you want to be taken for a person at leisure (but not obviously American), that's where you'll find the difference. The overall theme of the outfit should be more muted than flashy, but you should still have a bit of panache somewhere -- an interesting scarf or piece of jewellery for a woman, maybe a colorful wristwatch for a man. Shoes should be smart and practical but not obvious sneakers: a nice pair of Camper shoes would be good. Once you're properly dressed, your demeanor becomes key: walk the streets as if you are the master of the city, and not with mouth agape.
Finally, remember that you can communicate virtually anything in French simply by saying "Ooh la la!" -- it can mean absolutely anything, depending on the tone of your voice (enthusiastic, surprised, derisive, shocked, etc.). Just be sure to pronounce the first syllable like the vowel sound in 'no' -- but not the one in 'new' -- and you'll be in like Flynn.
A votre service,
Wideman