FBXL Social

It isn't the border, but that it needs more contrast with the piece. Even white would make it pop more. Same with the frame. Maybe try a dark brown frame that matches the edge of the piece. It would all pop more.

Other than white, maybe a pastel orange would contrast well with all the green, but it depends on personal color preferences at that point too
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OK, here's my vote:

As @Gnomeshatecheese suggests, keep the canvas next to the embroidery to give it space, then use a dark walnut color mat to make it all pop, and use the tan frame instead of white because it matches all the earthy tones.

The frame should focus attention on the piece.

Definitely frame it, as it elevates it beyond "oh, that's something I did" on the wall.