Yeah, I came to that conclusion after wondering why all these different tools would all be called sockets. It makes sense. "Socket" along with a descriptor makes better sense to me, though (i.e. socket wrench, socket driver, hex bit socket, etc).

Auchencrow, shall I gift you my random collection of slotted head wood, sheet metal, and machine screws? With drill drivers plentiful, I doubt I'd ever use them. Not to mention square drive wood screws beat the phillips head in most applications because the bit doesn't pop out.

Allen hex keys work most of the time, but often those 3-4" handles don't give enough leverage, for example crank bolts. And if you've ever done any auto disc brake jobs, you need the leverage of a socket wrench or breaker bar.

Roscoe,
The stem was probably fitted to the original owner when he bought the bike. The stem the bike came with was probably a 100mm. The bike shop not having a french sized TTT stem(very rare then and now), forced in a 22.2 stem. This was common in the early 70's. I did it, everyone did it.
The stem takes a 7mm allen wrench.
Get the old stem out- thats the hardest job. You may have to destroy the stem to get it out.
Then get a longer stem 22.0 sized. You most likely will have to use a french 25.0 bar with the new stem. But I have had good luck fitting 25.4 bars with old french stems also.

bwah, I wish I could jam a 22.2 in my moto's stearer. It just won't go in, not even with beer and swearing.

Just took a look at the pictures again. I bet there is less than an inch of stem inserted in the steerer. Maybe 1/2 an inch. Thats messed up. Try to loosen the bolt and yank it out of there.

Thanks for the details Chainring. I managed to find a 22mm/100mm but unfortunately it has ~25mm clamp.

If you are referring only to French sized stems, you may be correct. If all 3TTT stems, you are not. I have one that takes a 25.4 mm bar.

I was referring to the 3ttt Record (first gen). None of them that I've seen were marked. They very well may have been available in both 25.4 and 26.0.

I can't believe we're on 3 pages already, discussing an innocent old French stem (-if it IS a French stem).

- If on the other hand, if someone hammered-in the wrong, too-large stem, how could anyone not blame those infernal French?

Yuppers...that is the one I have. And it is not marked just as you say.

I think the TTT stem is true 22.2, but this size always measures more like 22.1 or 22.15 in my experience.
Typically well-worn calipers will, (if anything) measure on the small size, as the first few thou off of zero are thus lost to freeplay in the mechanism (I test mine periodically using a precision ball bearing or feeler guage blade, as the wear discrepancy cannot be zero'd out).

The steerer may have been reamed, possibly at the factory level, especially if the TTT stem was factory spec.

I'm curious if the OP's steerer OD is perhaps 25.4mm to go with the 22.2mm stem quill sizing?
Isn't just about anything possible when dealing with French/Euro bikes from the '70's?

BTW, TTT's clamp diameter is (officially, in all of their published literature and printed on their retail packaging) 25.8mm.
ITM (and others) have been made to 26.0mm, and ITM also made stems with a 25.4mm clamp, for lower-level racing bikes.

7mm isn't unusual in the context of vintage road bikes. Campagnolo used this size on C-Record crank bolts iir, and the Snap-On/Wrench Force alliance more recently made a "Campag" combination wrench with 15mm socket on one end, and a swiveling 7mm Allen hex bit on the other.
I've even found generic 7mm Allen keys laying around in bike shops, and my 7mm key is branded with the Bondus "hex" logo.