Cones!

Cones are the outer races of loose ball bearing wheels. They are a tapered nut(thus "cones") that trap the loose bearings against the inner races. Most of my old wheels are built with Campagnolo hubs and, as such, need little in the way of repair. Normandy hubs adorned many if not most French bikes of the vintage era and these don't enjoy the robustness of Campy.
If you dismount the wheel, remove the skewers, and spin the entire wheel between your outstretched hands, you can assess the condition of the hubs. They should feel smooth and frictionless. Some seem to spin endlessly, some feel dry and/or gritty. If you feel catches and notchiness, the cones or inner races are likely at fault. The inner races, integral with the hub, are less likely to pit but pitting of the adjustable cones is fairly common. Greasing and adjustment of the bearings might help but if catchiness continues there's something wrong. The repair is straightforward.
This is what pitted cones look like:

Cones for Normandy hubs are not easy to find. Knowing the model (Competition, etc.) would help but it seems some "plain" Normandy hubs had variations without obvious model nomenclature. Even if an NOS set show up, they may not fit your hubs. For example I removed the cones from a '75 Peugeot UO-8, a very common bike of the era, and though the hubs looked similar the cones were not.
The best way to tackle this is to measure your existing cones and go to http://www.loosescrews.com/index.cgi or a similar site and search for dimensions of some available cones. Typical French axles are 9mm X 1(diameter by thread pitch) in the front and 10mm X 1 in the rear. I used calipers to come up with measurements from the existing cones. Some come with seals and some don't. I found some Sansin cones for the front and some Shimano(with seals) for the rear. Diameter appears to be the most important followed by the depth. Within reason, the hub could be shimmed if the cones are too short. Thread and pitch must of course match your axle. It is a good idea to replace the loose bearings at the same time. They are not expensive. VBX even stocks ceramic loose balls in common sizes but I'm just not that pimp.
Here are the replacement rear cones:

These were not easy to install as the flats(for the cone wrench) were deep on the cone - even inside the rubber seal(how is that supposed to work?!). They were far too recessed into the Normandy hub to reach with any cone wrench. I've never rebuilt that specific Shimano hub so I'm not sure how the balls are so close to the flats and where the seal seats. Anyway, cleaning the threads of the axle helps and judicious use of needle nose pliers(when finger friction failed) helped in final placement. These are the problems you run into when trying to make non specific parts work - get used to it!
Unless you are shimming the hubs (from new cones that are too short) the wheel will remain centered in the frame when you are done. If shimming, you would certainly rather adjust the hub left or right evenly with shims than re-dish the whole wheel needlessly! Don't sweat it if you find perfect replacements. Mine were within a mm either way so it was fine.
A word on adjusting the cones. It's an art - not a science. If all slack is removed, they will be too tight once the outer nuts are secured. Even with slack the skewers will exert enough force to tighten them more. You have to play with it to get them just right but better a bit of play than too tight which will wear the hub out quickly. As of the first try, the rear has no play at the rim once installed (of course it could be a bit tight rather than perfect - how can you know?) and the front has too much play at the rim. I used blue automotive axle grease but there is cycling specific stuff out there that is supposed to be great.
Of course, there have been times when I've just swapped in a set of vintage Campy-hubbed wheels and called it good!
Good luck and feel free to comment if I have miscommunicated something.