In this case, things get complicated. Neither LH nor AF accept your breeds for travel in the hold anymore, and ever since AA stopped accepting pets as checked baggage in 2020, Alaska is the only airline left in the US still offering this - but they have an embargo on brachycephalic breeds and will not accept either of your dogs as well: https://www.alaskaair.com/content/tr...d-restrictions.

The only airline I know who still will accept your dogs in the hold as checked baggage and flies between Malta and the US is ITA: https://www.ita-airways.com/en_us/fl...trip/pets.html. ITA just 'recommends' not taking snub-nosed breeds in the hold but does not ban them.
ITA also has a 10kg weight limit for in-cabin animals, so at least your pug could fly in the cabin. In my experience with them, you could get away with the Frenchie as well, providing he/she fits in the regulation-size carrier. They'll allow both dogs in one crate for in-the-hold transport, too.
However, ITA has a very limited network and flies nowhere near Tulsa.Their only US destinations are on the East (Boston, New York, Miami, Washington) and West (Los Angeles, San Francisco) coasts. They'll add Chicago in April 2024. So it's going to be a very long drive to Tulsa.
All US airlines allowing pets in the cabin have no weight restrictions, just carrier size restrictions.But none allows more than one pet carrier per person, so flying domestically is out if you are on your own.

Apart from that, you'll have to cough up some serious money for getting them to Tulsa as manifested cargo using a pet shipper I`m afraid.
If you decide to go this route, check out Turkish cargo: https://www.turkishcargo.com/en/prod...-cargo/tk-live - AFAIK, they do not mandate going through an agent/pet shipper but allow you to handle the paperwork yourself, saving the considerable fees. They fly to Dallas, so try booking the dogs to there for the cheapest price as that will only be two segments (Malta-Istanbul-Dallas) all on their own flights.