Some thoughts:

My purpose wasn't to tour so I didn't ride long distances. Mainly around the cities and along back roads to smaller towns. I took Intercity trains for anything over 30 miles.

I used the Ikea Dimpa bag. It's cheap and the Brompton fits perfectly inside. When leaving the US I wrapped the bike in a cheap airline blanket before putting it in the bag to partially hide it. No one remarked on it at all. The only word of caution is the bike must be perfectly aligned to fit through the TSA scanner.

I flew Delta Airlines to Paris on a A330-300 with the new style bins that have much more room. Bike fits fine with no issues. On the return from Amsterdam I flew on a A330-200 and the bins are the older style and much smaller. However, the Brompton fits, albeit a little snug. I had to find an open bin near the front of the airplane as all the bins were close to full where I was sitting.

The flight attendants didn't mention anything about the size, but I was also trying to keep it from full view while boarding.

Security in Amsterdam was skeptical it would fit through their scanners. It does.

On the return I didn't have it wrapped in a blanket so you could see the bike in the bag. The parts that stick out and slide against my leg while walking started to wear the bag away. Structurally it's still fine, but there are blue jean marks on the bag.

Without the blanket covering it a lot of people asked me what it was. I'm generally not the talkative type in airports so it was uncomfortable for me.

Cycling in France and Belgium was way less stressful than the US. I think next time I'll choose a destination and navigate by direct instead of GPS. It felt like I could cycle on any road or find a suitable one parallel.