As far as I can hear from the video, the clock was out of beat when you had it going on the bench. Perhaps it is better now you have it in the case....? Clocks won't go well if they're out of beat and small French clocks like yours are very particular in this respect.
You day the 'fork which contains the pendulum' was too wide. Well, there is supposed to be a small amount of play in that fork between it and the pendulum rod. Again, it's hard to see from the video, but it looks to me as if you have closed it up so that the fork touches the rod. If so, that's too tight.
'Tiny pieces of cotton fiber on the escape wheel' were not helpful, but the whole movement is very dirty and badly needs a complete cleaning and oiling. The dirt is likely a large part of your problem. However, if you are going to see the clock, you could leave that for someone else to do. If your wife is worried about shipping it through E-Bay, why not put it on Craigslist and have the buyer collect it?
JTD
I did get it running on the bench, if out of beat then due to its circular frame and hard to line up perfect.
It has run all night back in it's bronze case. Seems to sound ok.
The fork was real loose. I had been thinking over 100 years of rubbing wear steel on brass.
My thought was the pendulum rod with too much play won't be pushing the fork far enough each way to keep the escape wheel running.
And was part of me trying to figure out why it kept stopping.
Rod still has some clearance., and is free in the fork, actually think it is perfect fit now.
My technique to tighten was, use a small screwdriver, slip into outer part of fork, then squeeze at rear of fork with vice grips.
This takes a somewhat delicate approach, the screwdriver keeps it from squeezing at the front which will form an angular pinch.
It is tighter and fork is perfectly parallel to each tine now.
Also the fork was slightly crooked, at an angle. To straighten, grasped in vice grips and tuned it leftward to line it up perpendicular to the frame.
The cotton fibers were my own fault. After I oiled the clock, I dried up extra oil using a cotton swab on the wheel, which left fibers behind. Had to use a lens and tweezers to pull them off.
My advice, don't use any cotton swabs. Using cotton was my attempt to figure out why it kept stopping, I was thinking could oil drops stop the escape wheel due to excess fluid friction. But I don't think so now.
Paper towels rolled up much better for drying excess oil.
Someone had been in this clock. And the bell was striking off 30 minutes, half hour bell struck on the hour and the hours on the half hours.
I pulled off minute hand and moved it 180* and now it strikes like it should, hours on the hour, and 30 minutes on the half hour.
This clock sat in wife's parents house since 1960's and I don't think they ever ran it. I never saw him run any of his clocks. I think he bought overseas when stationed in France.
Another clock I got from him is a Vienna wall clock from 1890. I had to oil mechanism and reglue and repair and refinish the wood case. I checked the serial and mechanism is from 1870, Gustav Becker.
Wife likes that one.
