On a more serious note: what's Vichy-France's political situation in HoI3? Is there an NA-pact or any treaty between Germany/the Axis and Vichy? In any case I can imagine that their thrat level must be very low for Italy.
IIRC there isn't. Vichy's threat to Italy is irrelevant anyway, because Italy's threat to Vichy + it's low neutrality means that Italy can DoW anytime.
That is one problem I see with the current DoW mechanic: it looks at both the target nation's threat to the declarer, and the declaring nation's threat to the target. Once you declare one war, you can essentially declare war on anyone else in the world.
Hence it is easy to go on a conquest binge with Italy in '37 - DoW Yugoslavia (the +20 threat due to core makes it easy) , and voila, you can practically DoW anyone else in the world. Of course, WW2 will probably start in 1937 against Italy, but that is another matter...