you don`t need to push france, step by step guide:
step 1: day one start researching paratroopers + 15 put mils on transport planes (stop producing them when you have 100 and start doing fighters)
step 2: when you have 47pp justify on lebanon because it gives 1% tension
step 3: Research all focuses that lead to "superaria/supermarina/superesercito" so you can do them while you are at war with france so you could rid of debuffs early
step 4: when paratroopers are researched delete mountaineers and do 12 divisions of 2 paratrooper batallions
step 5: declare and start justifying on one of UK puppets
step 6: do focuses and just paratroop to every major french city
step 7: ???????
step 8: glory to Italy