Very attractive, though the card seems to be overpaid. Someone here will know better than I.
My 1934 Postal Guide only talks about steamship service to/from Alaska, so I am guessing it went from Juneau to Seattle by steamship, then carried by air to (probably) New York. There was no regular transatlantic airmail service then. The agreements were to carry mail first by steamship to Europe. In the case of Italy, that would be via France (at least in 1934, but that seems to be the case in 1933). Those events would explain the somewhat long transit time to Paris overall. Then, with airmail service paid for (3c per half oz. additional for Italy, in 1934, perhaps more in 1933), this would indeed have been flown from France to Italy.
And perhaps someone can tell us about the "V"(?) marking on the back.
The first air mail service from Juneau to the US (Seattle) was June 22, 1940 so hy-brasil is correct that it would have gone by boat from Juneau to Seattle then likely get put into the domestic airmail system across the US then by boat to France then by train to Paris where it was backstamped at the Paris North Airport which indicates it would have gone by air either partly or all the way to Trieste. I agree that the postage seems to be overpaid for such a service but I am not an expert in adding up the various parts of the trip.