BISTRO/FRENCH FOOD SOUTH BEACH FLORIDA
There's no French bistro style on South Beach that I could recommend. Have heard good things about David Bouley's Evolution in the Ritz Carlton but it's higher end than bistro style. There's L'Entrecote de Paris around 4th & Washington but it's underwhelming.
If you're not fixated on French Bistro, there's a number of good restaurants in South Beach (search this board and you'll find many recommendations). If the concern is that the place not be too party-ish/loung-ish for bringing a client, consider Talula (23rd & Collins) or Mark's South Beach (11th & Collins) which have a more serious vibe and you can hear yourself talk (and excellent food).
French bistro is out in sobe A la Folie does not fit your requirements. Nemo and Prime 112 are other choices. Prime has excellent onion soup btw, but has a NY steakhouse vibe and is usually pretty loud. If you want quiet and good, the Fronesor's suggestions are a winner and so is possibly Nemo.
Joes stone crabs can also be a choice, but that is also loud. If you can drive a bit, the Forge might also be a good choice on 41st st.