There were MPEG-1 software encoders (e.g. CMPEG) & decoders/players (DMPEG, VMPEG) for MS-DOS that would run on a 386.
Bear in mind that frame sizes were tiny (e.g. 160x120), the display might have to be palettised for a 256-colour VGA display, and just because it runs on a 386 doesn't mean the frame-rate is anywhere near real-time! And the downloable MPEGs of the time were often video channel only.
I think mirrors of the SIMTEL archive still exist, so just go look.
Update 1: A quick search turned up an ancient FAQ describing VMPEG 1.2 for DOS as "high speed: e.g. 21 frames/s on a 386DX/33 for a 160x120 I frame sequence" so that would be your broad target.
I'm pretty sure Win3.11 already had Media Player, so again you should be able to view .avi on a 386 that way.
Basically, the trick is to downscale the video until your machine can manage it...
Update 2 (based on the comments): The issue with the .avi route is that it opens the can of worms that is codecs and compatibility. I had a rummage in some old backups and found my old Win 3.11 SYSTEM.INI, excerpt is:
My system had collected a few extra toys over the years, but you can see there's an AVIVideo driver defined and a list of codecs - VIDC.*. In the meantime, @DmytroL had a look on his laptop and (in a comment) reported:
I happened to have a codec management tool from K-Lite codec pack installed on my Windows 10 laptop ... The Microsoft Video 1 and Microsoft RLE ones are also present and enabled...
So, it should be possible to check SYSTEM.INI to confirm that the Microsoft Video 1 and Microsoft RLE codecs are installed in Win 3.x, and then create a suitable video on a current Windows laptop.
The difficulty will be that the OP has very slow hardware and so will need to keep both frame rate and size right down: even 160x120@10fps looks way too optimistic. I can't comment on which codec would be a better choice - try both and see. In particular, such an old machine is likely to have a very primitive graphics card - there will also be the overhead of quantising the output display down to a palette of 256 or even just 16 colors (for a stock VGA card).
But it does indeed look as though one can still create a video on Win 10 today that will be viewable on a stock Win3.11 system.
qv.exequick view (knows also Divx and sound but not sure if it runs on 386 as I used it later...) on 386 there was QPV for images (GIF included not sure if also mpg) and cant remember the old mpg and fli viewer names (it wasnt QV nor PV) however IIRC it was only 256 color and low resolutions without sound and only for small videos... it took ages to decompress mp3 to wav on 386 DX40 (like 30min for song)... IIRC games used bik format but not sure if also on386 or latter on