My friend recommended the Houses - Paris: 90 euros/night (two night minimum).  You need to email them (resa@thehouses-paris.com) to reserve.  My friend's comments:

It's a simple, small, cute apartment with a kitchenette, about 30 meters squ., great, generous-sized shower (none of that tiny plastic shell stuff.)

It is located in a ruelle/through-alley which is one of the secret gems of paris. It is really, really special. My Parisian friends were delighted and impressed, as the neighborhood has been until recently, traditionally immigrant and working class. There were so many Parisian 'tourists' making urban pilgrimages here to 'discover the countryside' in paris, even people leaving contact names on the building doors asking people to contact them if they wanted to sell.

The problem is, it's about an 8 minute walk in any direction to one of 2 or 3 metro stops. No problem if you don't mind walking.

Also, Homelidays (though a quick search indicates that most [if not all] offerings are by the week, rather than the night.)

Anyone know of any other such possibilities?

Truth unfolds in time through a communal process.

I don't know why there are no direct trains at night to Switzerland, all night trains include changing in Karlsruhe.