1. no don't bring the carseat on the plane - it makes them the perfect height to kick the seat and unless he's fully asleep you'll spend a lot of the time holding his legs down - all bad. I did a 14 hour flight with dd at that age and she just slept with her head on a pillow on her seat and her legs on me (with the buckle over her over a blanket). The CARES harness is quite good though for awake time / take off / landing. At least being under 2 you'd still be allowed to hold him if he refused to be buckled in his own seat. Once they hit 2 you HAVE to have them buckled in in their own seat for takeoff, landing & turbulence
2. No I think you can only gate check the stroller, granted I bring my sit'n'stroll to the gate and check it there, but I don't think they'll let you check 2 seperate things
3. just get him out in the sun and try to get back on schedule as quickly as possible (with nap times, etc) But really, just know it'll be a tough couple of days
4. I've never had a letter for dd and I've traveled back to the states twice with her. I don't think it's necessary
Yes, use a car seat on the airplane. fAA highly recommends it, especially during take off and landing, and during turbulence. Kids are large projectiles. Look on your airlines website though, US and Canadian carriers all allow it, but some international won't.
Yes, you can gate check a stroller, but it's not recommended to gate check your car seat, given how they're handled. It is allowed to check it though, usually you get to gate check two "baby" items.
No idea on the jet lag, mine always adjusted easily.
Yes get a notarized letter that gives you permission to travel solo, other countries are most sticky about this than the US is. Murphy's Law, you don't get the letter and you run into trouble.
1. No, I would not recommend bringing the car seat on the plane. I end up with DD on my lap for most of the flight anyway...Since DS is under two, technically he can be on your lap during take off and landing. When flying airlines other than US ones, they will provide a infant seat belt for your LO to use that attaches to your belt. I second getting the CARES harness. I have heard nothing but good things about it from my expat community and plan on purchasing one when DD is two.
2. I do not think you can gate check both stroller or car seat-but am not 100%. If you plan on bringing both, I would call the airline company or visit it's website.
3. In my experience jet lag is always the worse when you travel west to east than east to west. Try to get him to sleep on plane-especially the second half of the flight so that he hopefully wakes up after you land. We usually will spend the first day with DD taking her outside for a bit.(like pp suggested)
4. When I flew alone with DD, I did not have to show any type of documentation-but again I only travel solo with her to the States and back to the UK.
Enjoy your trip to France! We just got back from a trip to Paris with DD (She's 18 months and had a blast!