Im in the same exact predicament, with a Peugeot I'm fixing up. Not wanting to put in hours of my muscle and sweat into the rust removal of my French baby, I tried something new. Highly recommend Evaporust. The best deal is the gallon size I learned after buying 4 of the 32 oz. and the cheapest spot is Harborfreight. But you gotta have the 20% off coupon. Amazon has had it pretty cheap to.
Anyways, you soak any parts with rust and it comes off like butter. But doesn't smell, sting or anything. My issue now is finding the right container to soak my rims. Seriously should have my own line of bicycle restoration supplies. Im at the point where all the rust is off and now I see where the chrome is gone. I'm waiting on a quote from chrome plater, and checked out price on new parts, and checked out spray chrome also. I also am debating on what to do with the frame, now that rust is gone there are a ton of nicks. The last bike I painted was a b****. Excuse my unlady like language. Let me know what you do. But keep in mind if you do anything to the rim your gonna have to get all new spokes and that can be $$ and a whole new thang.