In randonneuring (specifically) there seem to be a couple schools of thought (and there are pros and cons to each):
traditional franco-centric / constructeur approach: lots of such bikes are seen here -
http://www.flickr.com/groups/classicbicycles/
road race bike plus accessories approach: the idea is to take a regular, performance road bike and add in some accessories and other minor equipment mods to make it a bit better for long distances.
touring or cyclocross bike approach: start with either a touring or cyclocross bike and make mods / add accessories.
endurance bike: there is sort of a new genre being marketed out there...these are bikes stylistically similar to modern road race bikes but the bike's design is tweaked to make it better for LD. some companies are entirely focused on this - Volagi for example.
Is there one that I am missing, folks???
(the one I take is different yet, still...
http://rothrockcyrcle.wordpress.com/...ndo-and-ultra/ )
Now, if you are interested in ultraracing, that's a bit different still - I don't think you will find many constructeur type bikes used for that (if any...)