Will slightly slimmer seatpost make a difference?
According to Sheldon Brown's site, there are 1987 Peugot Versailles with 23.8mm seatposts (and I have heard of other french bikes with 23.8 mm seatposts, so it is probable that you've measured correctly). The measurement should be done with calipers or a seat post measuring tool, though. 

One solution I've heard of is buying a 24 mm seatpost and sanding it down until you shave off 0.1 mm. Another is starting with a smaller seatpost (bmx for ex.) and trying to shim it in somehow (coke can or whatever). Of course this is all ymmv, but its quite difficult to find 23.8 mm seatposts. 

I'd probably just get the 23.4 mm one and hope for the best.