This is new info for me and thought others may find it helpful. I had an international plan when we last traveled to Europe but as fellow Verizon users know, the monthly plan is now $100 a month (and I think the month referenced by Verizon corresponds to your billing month period rather than a calendar month; someone may want to chime in about that). With an upcoming 7.5 week trip, I'm not likely to use that plan.
I read an Apple-user post on some other forum about the user getting unexpected roaming charges when traveling AND they had turned off roaming. I checked the settings referenced in the post and see the "fine print"!
In the iphone, go to Settings and then Cellular. Scroll to the end.
Under Wi-Fi Assist, you should see "Automatically use cellular data when Wi-Fi connectivity is poor." Mine was on but is now off.
Under iCloud drive, you should see "When not connected to Wi-Fi use cellular network to transfer documents and data." Mine was on but is now off.
I would think that if you leave your phone in airplane mode, there would not be an issue. But it seems best to check these other settings as well.
Please correct me if I'm wrong on this!
Also - it's probably best to turn Cellular Data off as well.