Pictures indicate two road bike frames (and an old mountain bike frame tossed in for good measure) each approximately the same size and head tube angle. One frame has an original fork, the other none at all. I have a spare fork that would fit the forkless frame, BUT... does it appear to have too much rake to it? I see the mismatched fork would put the axle out further by a significant amount as compared to the stock fork on the other frame. The Concorde designers saw fit to have a certain rake for that frame. I would have swapped forks out if it fit the Sekine (blue one) but not enough thread protruded.

You can change rake as long as the axle-crown measurement stays the same. In fact, if you can live with the headtube angle change, then you can change the A-C too

I'm sure you will now get that advice repeated to you by others

Without real numbers all this is speculation and opinion. Amount of rake or head angle, or BB drop, or front center WRT rear center (and a bunch more specs) taken as single aspects is no path to understanding. Also how much rake (and it's resulting trail) is right is a topic that many have spent a whole lot of time on with no widespread agreement.

Now lining up complete bikes side by side to compare fit dimensions is a worthy goal. But that's far from what was asked. Andy

If you're adding rake you're reducing trail. You can get that trail back by slackening off the head-angle a bit which would happen if you used a headset with a higher lower stack height. 10mm of extra rake can be compensated for by about 1.5 degrees more slackosity of the head angle which you would probably get by about 10mm extra lower stack, making your TT imperceptibly non-horizontal. But it will probably ride fine though a little differently if you just go with less trail.

Equal trail but achieved with slacker head and more trail will make the handling mostly the same, but you will have a bit less wheel flop. This is often how tourers are built because a bit less wheel flop is considered desirable if you have bags on the front.

I also kind of think a wider handlebar means you want more trail. Modern MTB frames have really wide handlebars and loads of trail and feel "normal" to ride.

If you post actual numbers of fork offset, head angle and wheel-base I can attempt some math. But long story short it will probably be fine and, if not, adjusting the lower stack is an option. This parameter often gets randomly adjusted when people buy new headsets anyway.

Build the bike. Ride it. See if you like it. It doesn't matter what the designer intended, if you like the way it rides.

Too much knowledge is a bad thing. Most people couldn't even tell the difference after the bikes are built up..

Ok, thanks to all for the input on this. I'll see about measuring the headtube angle on the frame. The fork is from this bike. Attached is a picture of just the 25" Sekine frame and said fork. The fork is a Tange and has a nice Chromoly "ring" to it so I figured why not use it, particularly for the cantilever braze-ons. They might make for a nice front mini-rack mount. The fork crown is also through-drilled for a fender (or brake). This bike looks like it could resemble a Peugeot U0-8 when done. Maybe it'll ride the same.