It looks like with those racing brakes you wouldn't be able to fit bigger than a 700x28 on the resultant bike. The correct French word to call this style of bike is audax instead of randonneur.

My suggestion for skinny tires is, as always, the Vitus 979. They are basically free off Ebay, they are comfortable, they are fast, and they are light. My personal experience is that mine gives me wings. I'm 6'2 and 170lbs and I've had a 60cm Vitus 979 for a couple years now, riding mostly roads but some occasional hardpan gravel. No problems in the frame department! I think it'd be quite easy to throw a Nitto M18 on there with P-clamps as well.

Others don't like the Vitus 979, but that's why this is a forum

If you're planning on trying to fit fenders in there, then maybe a Bridgestone RB-1 or old race-y Trek, the thinnest tubing you can find, like 531 SL. There are lots of good specs on the old Trek frames at the vintage-Trek website.