Your starting point for vintage does not need to be insanely expensive or even European. Late '70s to mid 80's Treks in Reynolds 531 or Ishiwata 022 are going to be well within your price range, as will Peterson-era Bridgestone road bikes (RADAC, RB-1, RB-2, RB-T, XO-1, XO-2). Handling of those makes tends to be pretty neutral, particularly in the case of the Bridgestones.

Italian bikes are different in character, even when the are built from the same tubes and use the same parts groups. Some have handling which is just way too fast outside of the peloton, and so are not fun to ride unless you drink way too much of that horrible espresso like the Italians do. Tommasini and Rossin are two that got it right and have good artisan build quality (particularly the former). Other names to consider (though you'd better ride them first) are Masi, Colnago, Frejus, De Rosa. Columbus SL rides the best, with the SLX slightly behind it.

French bikes require French parts or a hell of a lot of intrepidity. Since many of the French parts were, shall we say, merde (oh, Simplex, why did you think Delrin was a good idea?), the intrepidity is required more often than not. It allows you to retrofit SunTour derailleurs and extra-duty Sakae Ringyo or Nitto stems in place of the evil AVA death stems that too often came standard on those bikes. The payoff is ride quality. Very few bikes can match the smoothness of a PX-10 or Grand Jubilee.