Your seat tube walls are about 1.4mm thick, which indicates a plain gauge carbon steel frame, rather than anything higher-end or more exotic. A Peugeot PX-10, with the same 28mm seat tube OD you have, takes a 26.4mm seatpost. My two Capos, both full Reynolds 531 and both with 28.6mm seat tube OD, take a 26.4mm seatpost (straight gauge frame) and a 27.2mm seatpost (double-butted frame). I would expect a straight-gauge 531 French frame to take a 26.4-0.6 = 25.8mm seatpost.
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"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069