Oooh you can tell who has experience of village life and who doesn't here!
Do NOT go round or write her a letter - if you do either, then it will be 'she came to my house to harrass me' and 'she wrote me a nasty poisonous letter full of lies'...
Then the drama will be her twisting things you have actually done, and it becomes harder to refute anything as it muddies the waters.
Go to the things you go to, talk to the people you normally talk to, I'd be in the pub, often and IF anything is raised...and if she is batshit then chances are she will come in, throw drama and run off and people will ask 'wtf?'...
THEN you can say 'not a clue, she appears to think I am someone from her year at school, but I went to a totally different school, different location, different year, so she's clearly mistaken'...
And that will get round the village fast because 'new woman is being weird about Highfivemum and making up stories' is exciting weirdery!
If she has just made a mistake and realises it, she will belt up and behave and not mention it again out of embarrassment and things will all go back to normal relatively quickly.
If she IS batshit and persists, then the village will spot this quite quickly as long as you leave her to dig her own hole!