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Hi I'm a new member and this thread caught my eye.
Touring on fixed is certainly possible and desirable, I've been doing it for years. As long as you don't overload the bike, true even with multi-geared bikes, any terrain is do-able. Last year I cycled all over California, a place with extreme changes in altitude over short distance with light camping load. I took the Tioga pass at 3032 metres on a 48X20, 64 inches. I only used a front brake but would recommend using front and rear as descending long passes can cause the front rim to get very hot from brake friction.
My bike has no braze-ons either, for my US trip I carried luggage in a Carradice longflap saddlebag, few clothes, 3L waterbag, army messtin and bivvy bag with a 1 man tent strapped to lid of saddlebag. Used small rack designed for use on front of bike, ie shorter than normal rear rack but ideal for saddlebag support and p-clips have never let me down.
Enjoy your trip to France