"Un caf� l�ger" will probably get you what you want, but it can get rather complicated depending on what kind/volume of coffee you want.
Generally, in France, if you ask for "un caf�", you will get a very small cup of strong coffee and no milk.
If you want a larger, milky coffee, ask for "un petit cr�me" or "un grand cr�me".
At breakfast, you would normally ask for "du caf� au lait, s'il vous pla�t" and you would get hot milk served separately in a jug.
In Belgium, where I live, if you ask for "un caf�", you will get a medium-sized cup of coffee with a small pot of cream. If you want a small, espresso-type coffee, you need to ask for "un petit caf�" or "un expr�s".
In any case, if the coffee is too strong for your taste, you could always ask for "de l'eau chaude, s'il vous pla�t".