My grandmother said you may be able to darn the mesh using a navy thread. She said that they use to repair socks by darning the hole. She said it was very common in her day. Probably a video on YouTube. She also said there are cloth press-on (not iron-on) patches. After you darn the shoe, cover the patched area on the inside with one of the press-on patches cut to a little larger than the hole and where your toe rubs the mesh.
Yes - get needle and heavy thread (doubled) and sort of "re-weave".
Then maybe superglue a bit of cotton cloth underneath to protect it from tearing again.