I'd like to find an easy way of reading and writing files (stored locally) from my program running on a localhost server. If I use const fs = require(fs) it can't find the Node module from the server. This makes sense. Is there any way of accessing that file from my javascript easily, with similar functionality to the fs module?
It appears that you aren't quite understanding how the client/server architecture works for an http server and the browser.
There's an http server that runs in nodejs. That has access to the local file system using the fs module. This is server-side code that runs in the nodejs execution environment.
There's an http client (the browser). It makes an http request to your server, the server sends back an http response and the browser gets that response and processes it. If the request is for an html page, then the browser gets that HTML, parses it, displays it and then runs any scripts embedded in the HTML page. The scripts running in the HTML page are running in the client/browser (not on the server).
Javascript running in the browser does not have access to nodejs modules like the fs module. It only has access to the libraries that the browser makes available. Absent special browser add-ons (with elevated privileges and associated security risks), scripts running in the browser in HTML pages do NOT have access to the local file system. This is for security reasons as you don't want random web pages that just happen to click on to have access to anything on your local hard drive.
So, you generally do not access local files from your browser Javascript. Instead, you either store data in LocalStorage and fetch the data from that or you store the data on the server (on behalf of the specific user) and that data is either included in the web page (so the Javascript running in the web page can use it) or the data can be requested from the server by the browser Javascript (using Ajax calls).