How do I finish this table?

If you want them to blend in, paint them the same color. Personally, I'd cut them off.

You can add a strip the same height as the bottom piece just a little bit wider so it bumps outward about 1/2 inch. Glue on with with wood glue and paint white to match or make them stand out with the same color grey the you used above.

Sarah... unless it would seriously impact the the height of dining at the table, I'd simply cut them off! If it does, Em's idea would be an easy, workable solution!

I think another coat of paint to get a more covered and smooth surface might do it I like the legs they have a nice look

Will the table still be a good height if you cut them off? If not you could add trim around the bottom to hide that funny part.

I would cut those bottom pieces off. The legs would have a nice finished look without those bottom pieces hanging around.

I personally like the idea of trim around those odd pieces at the bottom of the table . it would give the table a more finished look . I am betting that is what was there before .

It looks like there were some flat platform bases that those slipped into. If your handy you can make something similar. Otherwise cut them off.

Here is are similar tables

https://www.hometalk.com/diy/paint/furniture/rustic-farmhouse-trestle-table-makeover-24443180

https://www.hometalk.com/diy/paint/furniture/prepping-furniture-for-paint-or-stain-12809853

I'd add a simple trim all the way around the base and paint same color.