What should I do before breeding my pure breed Labrador Retriever?

Take her to a few dog shows first and see if the judges like her. If they don't like her then she's probably not breeding quality.

Get her hips checked (with the OFA) and get her eyes checked by a vet. Make sure she has a healthy diet and make sure that the pups get adequate prenatal care.

You seem to be doing everything right so far- many people don't put any thought at all into breeding their animals.

She can't be certified with the AKC unless her parents are also certified.

For a male, get a registered dog with a show record- preferably a champion with good hips and eyes. Don't go for color over quality, but if you tell me the color of her parents and the color of the male and his parents, I can tell you what the chances of each color for puppies is.
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The AKC will not recognize her. There are not many French registered purebreds here. Most other registrations here are garbage. Even if she could be registered with the AKC (thanks to having AKC parents), we would recommend you get her champion titled and checked out for no genetic defects, then mate her to a male that has the same. At this point though, if you bring her back to America, you might as well just get her spayed. There are plenty of non-registered black labs over here do not have homes.
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First and foremost it take YEARS to learn everything involved with breeding and by the time you do learn she will be too old to breed for a first litter.

Find a reputable breed mentor and you will learn all that you need to know from them

No matter how prepared you are a pregnancy is ALWAYS a risk. Even reputable breeders have lost females and/or the litter

The only way you will be able to register her with either the AKC or the UKC she must be registered with Société Centrale Canine first.

Labs are VERY common in the US and honestly if you are intent in getting into breeding. Have your current female fixed and start fresh ONCE you get into the states.

National breed club
http://www.thelabradorclub.com/
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Its great that you are asking questions before doing this. There is alot involved in breeding. There is no guarantee of no health risks. You have to ask yourself it you are you prepared to lose her for a litter of puppies? Are you prepared to lose some or all of the puppies? Can you cover the medical expenses if something goes wrong? Are you prepared to take responsibility for the puppies for the rest of their lives (if homes are not found or if they are returned).
Your dog should have her hips, elbows, eyes and cardiac testing done. You can have DNA testing done as well. These are expensive but it lowers the chances of passing hereditary diseases to future litters. Info on testing
http://www.woodhavenlabs.com/breeding.html#breeding
http://www.woodhavenlabs.com/clearances.html
Labs are extremely overbred, there OVER 125,000 Labrador Retrievers registered with the American Kennel Club and that is just one registering entity. There are over 25 worldwide. Personally, I don't think any dog should be bred unless they have something significant to offer aside from being a great pet dog. A dog should have at least be shown or competed with titles before they are bred.

http://www.justlabradors.com/forum/ has a ton of information on labs and breeding.
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http://www.justlabradors.com/forum/index.php/topic,34657.0.html

Yes, you can get an AKC number. But remember, purebred doesn't mean well bred — just because she's french doesn't mean she's breeding quality.

Has she been shown to her French/international championship? Do you have plans to obtain her AKC championship? Just because you think she's beautiful doesn't mean she's breeding quality, as most people can't evalute how proper her head is, what is her reach and drive, is her angulation proper, and what about the length of her upper arm? If you're not sure what I mean, this means you aren't the right person to evaulate her.

What tests should she have — for starters, OFA certified hips and elbows, possibly patellas as well. OFA thyroid for sure, possibly VonW, definately eyes CERFed clear. Possibly PRA (genetic test) as well as well as OFA cardiac cleared heart. None of this is cheap, and all of it on top of a championship — international or american.

Also, you won't know if she can bear puppies until she is actually trying. Have a reproductive vet on call for a c-section. You don't think you'll ever need one, but guess what — I"ve had to do several that I never expected.

The best thing is join the american lab club, get to know people, show your dog, find a mentor to help you pick out the right male (not just purebred, and not even just because he's a champion, but the best possible match for your girl). Save your money — a stud fee is approx $1,200. C-section if necessary, same or more. Remember, when the pups arrive, you put your life on hold for 3 or more weeks — no leaving them alone. No work, no school.

Then be ready to be responsible — guarentee the pups and take them back if their owners can't keep them — not just for a year or so, but for the whole 12-16 years of their life. Be prepared to refund money if there is a problem. Be ready to be a resource to them if they need any help, night or day. That is being a responsible breeder, and it's not always fun.

I know it sounds harsh, but if everyone did this, there would be NO unwanted dogs in shelters.
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show breeder

Dogs from foreign countries are registered with the AKC all the time
I have/had several over the years.
It is necessary that she is registered with an FCI recognized registry.
I believe in France it is this one.
http://www.scc.asso.fr/

Now the problem, the Labrador Retriever is the most over bred breed in the US, and statically only 50% of any given litter ever get sold leaving the other 50% to be disposed of one way or another. With such a market glut of Labrador pups there is just no sense in breeding them at this time. I have an 8 year old titled b*tch that has never been bred simply because there is no point in doing so.
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