Don't be afraid. You'll make it. Your cat will make it.
Recently I've moved to Paris with my wife and our cat. There were companies taking care of moving pets internationally, but we decided to do it on our own. While you need to prepare lots of things, in this post, I will focus on documents and process. Although this is not a complete guide for all cases, it will help you understand the process and what to search for in your case.
I was moving "to Europe". So I needed to understand what Europe asks for. I googled with keywords like
Europe pet non-commercial move from non-eu and found this web page:
Let's go through the document one by one.
My vet has implemented a microchip for my cat and gave me the microchip certificate. I need this certificate.
Read the details from the document. This has to be done at least 21 days before departure. Of course, I need this certificate, too.
My cat didn't need this because we were in Singapore. Refer to the Exceptions chapter.
This part is very important. From the web page, click "an animal health certificate".
I gave this form to my vet and he filled in all the fields. And it's not done. I had to visit Agri-Food & Veterinary Authority of Singapore (AVA) to get the health certificate endorsed by an official vet. I didn't have to go there and just do it online by myself but I strongly recommend you to visit there. They will help you go through all the process on the website from signing up to filing the application. After the endorsement, the health certificate is valid for only 10 days. To prevent odd cases like you miss your flight, schedule things close to your flight.
You may think these are all the documents required. There is, however, one another thing to be taken care of. It's an export permit. I was technically exporting an animal out of Singapore. It required me an export permit. To obtain the permit(license), I needed to visit AVA.
You can visit AVA and take care of both export permit and endorsement of health certificate at once in a day.
Now the documents are ready. You should also be ready for other things. Let me give you just two things.
If you want to bring your cat in cabin(which you really should do!), you need to check with your airline. Not many airlines allow pets in cabin. They charge you extra cost. Container size matters. I personally used Sleepypod Air and this is certainly not an advertisement. And your airline will have a limit of total weight of your container and your cat. The information on Air France can be found here. You definitely need to call airline first before purchasing a ticket or container.
You don't want your cat having a toilet problem during flight. So you'd better feed your cat so much less than usual. My cat went through 14 hours direct flight and couldn't pee at all. I brought a small plastic box with litter inside it. During the flight, I brought the container and the box into the toilet. I locked the toilet door, let my cat out of the container in the toilet, fed her, gave her water and let her use the toilet. She ate but didn't drink, pee, or poop. If she ate or drank too much before the flight, she could've suffered more.
It could be a difficult journey especially if it's your first time. Be prepared. Do enough googling. Make phone calls. But don't be afraid. You'll make it. Your cat will make it. I wish you good luck.