I thought I'd take a second here to update you all on what I learned.
Thanks to JohnnyRockets pointing me to a similar, older thread, I found a
very useful blog post by Gary Leff about this exact issue.
Gary had actually spoken to a spokesperson from Air France who agreed that "an airport ticketing requirement is not appropriate for the US market as so many people live so far from Air France ticket counters". I reached out to Gary via email and he was kind enough to give me the email of someone at Air France who was actually trying to put a stop to this.
Today I tried again, making the exact same reservation online, preparing to see the dreaded error message, but instead... it went right through!
I don't know what else has changed... the Flying Blue account is now a whole four days old, so maybe that helped, or maybe Air France really did turn off this draconian "fraud detection" algorithm. But for what it's worth, I did get the flight reserved and ticketed.
By the way, while I was going through this process, I discovered something that surprised me, which some members here might find helpful:
* When I navigated directly to flyingblue.com and signed in, then chose "Book an Award Ticket", I got taken to the Air France UK site (the URL was airfrance.co.uk and it said United Kingdom in red on the left). At this point when I looked for availability on the flights I was interested in, the only seats available were for 42,500 miles (outbound) and 81,250 miles (inbound).
* However if I switched to the Air France USA site and searched for the exact same route, I found availability at 25,000 miles (outbound) and 42,500 miles (inbound) ... a huge savings.
I don't know if there's a general rule about different availability from different versions of the website (US vs UK) but I wasn't expecting such a big difference.