A typical French salad dressing consists of a mixture of vinegar and oil (generally vegetable oil in the north and olive oil in the south); within France this is known as a vinaigrette (from the diminutive of the French word vanaigre, meaning vinegar). This can be found in almost any medium-level restaurant in France.
At home, and in nicer French restaurants, additional ingredients are added, such as herbs or garlic. The exact ingredients and quantities depend on the individual cook as there are no official "French Salad Dressing" recipes.
Outside France, the term "French Salad Dressing" is often used to describe salad dressings which are French only in name, and which would only be found in France if imported (at which point one can imagine many French people would be rather bemused to see the title "French Salad Dressing" to describe something quite foreign to them). In the USA and Canada, the term "French Salad Dressing" is often used to describe what is essentially a mixture of oil, vinegar and ketchup.
Basic Recipe - Simply oil and vinegar, as described above. I prefer a high quality olive oil.
Traditional French Salad Dressing - A traditional recipe based on white wine vinegar.
French Salad Dressing (Mustard) - Ready in 5 minutes and goes with most salads. Don't be put off by the mustard, this is actually a soft and smooth salad dressing.
Because oil and vinegar do not mix well, they are often served in separate bottles; each person pours onto their salad first from one bottle and then from another. In a medium-priced French restaurant, a vinaigrette is typically served in a pair of very basic looking square bottles, often sitting in a metal holder so that both can be carried together.
If you are purchasing a oil and vinegar set for your own home, one can also find rather more elegant bottles. It is also possible to buy a vinaigrette bottle which has two compartments (each with its own spout), so that both ingredients are within a single bottle. In particular I like the bottles which have an inner compartment and an outer compartment; if one places a olive oil in the inside chamber and a white vinegar in the outside chamber, the resulting appearance is quite attractive (although sometimes rather more difficult to manage than separate bottles).
It is also possible to server a French salad dressing in a single bottle. However, if one uses the basic recipe (just oil and vinegar) they do not mix well so each guest will have to vigorously shake the bottle and will then have a few seconds in which to quickly pour the dressing before the ingredients separate (an activity which hardly befits an elegant dining experience). With some of the more elaborate recipes, the additional ingredients (e.g. soured cream) may bind the oil and vinegar together, so the dressing can be served in a single container.