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.