improving Photo resolution for printing

On the Image Enlarger site https://www.imageenlarger.com/

do the following.

• Click the "Close File" button to upload your jpeg image.
• Then enter a zoom factor - try 2 or 3. Larger zoom factors will probably create a very blurry image.
• Then click the start button.

You will now see several variants of the enlarged image. Pick the one, that has the best quality. Depending on the interpolation algorithm the resulting image will differ slightly. Compare the edges around small details to pick the best result. Then click the image you like.

Dimensions: 360 x 345

This is very tiny. If you zoom it by a factor of three, printing it at a size of four inches at the longest edge will be the best you can hope for. Is there any chance to get a better copy of the image with more pixels?

I cannot test with Gimp right now, because it is hanging, since I upgraded to Mojave.

But the online Image Enlarger might do, what you want to do. It will increase the pixel size of a photo while preserving the sharpness of the edges, as much as possible:

https://www.imageenlarger.com/