I just pulled the bottom bracket out of an older Peugeot road bike and I'm trying to figure out what type of threading it has. I would like to replace the bottom bracket, since it is older, beaten up, and loose bearings. Since they are prevalent and inexpensive I was planning on going with a sealed-bearing Shimano BB.

1) How do I figure out what type of BB I need? I took out the non-drive side BB cup and it screwed out in a counter-clockwise direction. I was talking to someone that was telling me you could tell if it was English threaded or not by the direction you turned the cups in - is this true?

2) And on this topic, the drive side isn't "cup" meets flush up against the BB shell and just has two flats on it. I'm not exactly sure how I take this off. You can't get a spanner wrench or anything on it, I don't think. Suggestions?

Happy Friday! I hope it is warm enough somewhere out there for people to be riding outside. I'm stuck with rollers and working on old bikes...

Left (non-drive side, adjustable) are all generally right-hand (standard) threaded. Your friend was likely talking about the right (drive-side, fixed) cup, which for modern bottom brackets is left-hand thread for British/ISO and right-hand thread for Italian.

I don't know a lot about French bikes, but your Peugeot likely uses the now obsolete French threading, which is different than the British/ISO and Italian standards of today.

Bottom bracket sizing: https://sheldonbrown.com/gloss_bo-z.html#bottom
French bottom brackets: https://www.sheldonbrown.com/velos.html#bottom

You may be better off inspecting the cups and spindle races and if they are okay, then just replace the bearings.

Edit: Oh and it is supposed to be the nicest weekend we've had in months here, but I'll be stuck inside with the flu.

Your Peugeot almost certainly has French cups (if they're stamped 35 x 1 you have confirmation), and if you can save/service them, I'd recommend it. There was a recent thread on this forum discussing French BBs - you should refer to that.
The spindle tends to pit before the races, so perhaps you can find a replacement spindle and put in new bearings. If so, you should leave the fixed cup in the frame. French fixed cups thread in clockwise. That means that the bearing spin direction tends to loosen the fixed cup as you pedal. If the cup is presently in good and tight, leave it that way.
If you must remove it, you'll either need the proper wrench (see Park Tool) or, preferably, clamp the BB flats in a good bench vice and carefully turn the frame.

Thanks for the information. I talked to a good mechanic at a local shop today and he said everything looks to be in good shape on my BB. I'm going to reuse as much of it as I can, at least the cups and bearings, which are in good shape.

I might possibly have to change the spindle, since I am converting this to a single speed and might need a different length. Also, I'm going to try to use an old Shimano road double crankset as a single and not sure of spindle/CS compatibility. I'm going to try it all out and replace as needed.

My LBS charges $.05 per bearing. For $1.10, it's not worth using the old ones. (IMO)

Yeah, reuse the big stuff, but you might as well replace the bearings. That will probably extend the amount of time before you will need to repack again.

My mid 80's P6 has an English threaded BB, seattube and headset are french

The BB threads on a Peugeot can be French, Swiss or British, depending on the age. If the cups and spindle are not pitted, all you need to buy is 22 1/4" balls and a tube of grease. Leave the fixed cup in place.

I'm guessing that the fixed cup can be left in place while I remove and replace the bearings? I have never worked on a BB with a fixed cup. Since that is what people suggested, I'm guessing it is possible to take the bearings out via the opposite side?

Yeah, I'm trying to keep this rebuild inexpensive so reusing as much as I can. Thanks for the info.

I'm hoping I'll be able to find a new seatpost, as the current one is one of those big, clunky funny sandwich clamps, but the post diameter is small and weird...like 24.0 mm.

Uou might need a magnet to pick up the old BB's from the DS, depending how gunky or dry the grease is. It's rather hard to really examine the race of the fixed cuo without removing it, but I guess you could shine a light in there and hope you have better eyes than mine. (likely)
You can use grease to hold the BB's to the spindle when reinserting. Have the adj. cup packed with the bearings and ready to spin back on.

Yes, you can clean out the fixed cup with it in the fame; just reach in with a rag from the other side.

Good luck finding a new seatpost--it's getting nearly impossible to find anything below 25.0mm except 22.2mm (7/8") and 23.8mm (15/16" and this one won't be any better than your current one). Unless you're willing to spend $70 on a modern 24.0mm post (https://www.yellowjersey.org/frogstem.html), your only bet is a 22.2mm BMX post with a custom (or homemade) shim. If your current post works, use it.

If the spindle is in good shape you might be able to flip it around to improve your chainline without shopping for a new one. This is common practice on SS and fixie conversion jobs.