You'd probably need to give it a land connection to the main Swiss territories then, perhaps a fairly large chunck of Upper Alsace.
In my own TL I do add a chunk of the Sundgau to this new canton.It's not that far - about 25km to the nearest border with Switzerland (next to Basel). And much of the Sundgau was and is quite sparsely populated. A "finger" could easily be extended to Mulhouse without too much disruption, or the new border could stick out along the German border, instead of extending solely into France.
I was thinking that they gave Geneva an overland connection to the rest of Switzerland, even though it already had an access route across the lake, so why wouldn't they do that for Mulhausen -- which lacks the lake option, after all -- too?Or just leave it an enclave - by the end of the Napoleonic Wars, that was still a thing.