Lufthansa, Air France have the best pet policies for pet air travel. KLM too iirc. (I did this with three cats from India to USA)
I picked Air France because there was no layover and we’d all arrive and land at the same time. I wanted to be in the same flight with them at all times. They let me spend some time with them at CDG during the few hours stop.
I chose not to sedate my pets. I do not recommend it. But I speak for cats. Check with your vet. The pet cabin in the cargo belly is set up in terms of temperature and pressure for the pets comfort. You need to get airlines approved crates. Ours were comfortable enough for them to walk around and sleep. I did not feed them either. Because I did not want them to pee or throw up in the crate. But I left water. And I checked on them at CDG.
One thing tho’..and maybe this has changed now… I was asked to microchip them twice. Because the American format is different from the European standard. I also had to vaccinate them again closer to the date of departure.
You likely won’t have to jump as many hurdles as I had to because moving them from India required a lot more hoops. Between two western courtries should be fine as they’d likely accept each other’s pet passports.
If there were no other pets being flown, I could have possibly had them with me in the cabin. But my pets are vocal and everyone would have had a miserable time. Depending on your dog’s personality you could possibly book a seat or four for yourself but it won’t be pleasant for the dog. You’d probably be asked to muzzle your dog.
Having said that..chartered flight and possibly splitting costs with friends/family seems to be the better option. Good luck. Best wishes for a safe journey.