One interesting idea might be to ask your student to try re-implementing different parts of the web ecosystem, which would naturally involve using JavaScript.
For example, one project might be to guide your students through writing a simplified version of libraries like React or Angular -- probably after having your students use those libraries directly so they know what they're trying to emulate. This can be an opportunity to teach about some of the more interesting programming paradigms like functional reactive programming. (React was originally written in Ocaml, so you could maybe dovetail things there).
Alternatively, you could instead turn this into a mini compilers or parsing lesson: when writing React code, you can optionally embed HTML-like expressions (JSX) in your code. You could maybe explore having your students write a pre-processor for JSX: parsing and manipulating AST representing HTML-like expressions is probably going to be easier then manipulating ASTs representing full-fledged programs. (The one complication is that JSX is intermixed with JavaScript. So, to simplify this assignment, you should probably provide a regular JS parser the students can hook into/invoke.)
More broadly, I think teaching your students how more complex libraries or framework work is likely to be a more valuable and long-lasting skill compared to just teaching whatever language or library is trendy today. I don't think it particularly matters which library or framework you're implementing: the main value comes from the act of exploring some non-trivial implementation, and from "peeking" under the layers of abstraction we're already used to. And if you can give students exposure to JS (or whatever other language) at the same time, great.
A somewhat different idea is to double-down on compilers-related stuff -- JavaScript is actually a somewhat common target language (e.g. see languages like TypeScript or CoffeeScript that transpile to JS). For example, you could start by transpiling some homespun language into JS (or a simple language like lisp), then ask them to write an interpreter for their custom language, then finish off by asking your students to write a compiler generating webassembly. There's a lot of existing tooling/scaffolding you could probably use here to try and smooth out some of the rough edges. And to keep things simple, you'll have the student implement all of this in JS (or maybe TypeScript?), because why not.
The main disadvantage of these ideas is, of course, that it'll likely take a non-trivial investment of time to pull off. If you have only a few weeks to cover JavaScript, you'd likely need to significantly scope these project ideas down, or just not use them altogether. As the others have said, you'll probably want to avoid gratuitously welding two unrelated CS topics together, or avoid giving your students the "frankenstein" experience.