My dogs' results are pictured at the bottom.

OFA stands for Orthopedic Foundation for Animals. This group tracks, records, and certifies a plethora of established health problems, across all breeds of dogs. Here is the French Bulldog section on OFA:
My goal is to have all my breeding dogs tested so that I can make the most educated choices possible, and also pose the least possible risk for producing health issues in my pups, for their sake and for that of their loving new homes.

Hips: OFA hip specialists, picked at random from a board of approved veterinarians, evaluate very precise radiographs taken and sent directly from my veterinarian. Dog must be sedated. They look for depth of socket, space and laxity, as an indicator for likelihood of hip dysplasia. At 1yo a dog can get preliminary results, at 2yo they can be certified.
PennHip accomplishes the same task, but in a more objective, measurable fashion. It can be measured accurately from 5 months on. It's about 5x as expensive. Veterinarians require special training to provide PennHip evaluation. They sedate the dog and then use a tool that measures exact span of movement in different positions of the leg. Then a decimal score is given, and a graph indicating where on the breed's average your score falls.

OFA Trachea: a radiograph is provided to a randomly chosen panel of OFA veterinary specialists, showing the dogs trachea, so it can be evaluated for hypoplasia, where the esophagus telescopes, curves, or folds and can cause problems with breathing, regurgitation, and other problems.

Patellar: the vet manually palpates both kneecaps in a normal physical exam, and if he can move one out of place by force at all, it is considered lax and a possible Grade 1. If it moves out of place on its own intermittently but causes no pain and requires no intervention, it's usually a Grade 2. If it persistently stays out of place and could require surgical intervention due to pain, it's a Grade 3. This is one of the most prevalent problems in small breeds, known as luxating patellar, or slipped knees. Thankfully, Frenchies have so much muscle mass, without the heavy weight of a large breed, that even with this problem, and/or hip dysplasia, it is usually much less severe and less likely to be debilitating as it is with large breeds. Unfortunately, this means that a lot of breeders are careless about it.

OFA Cardiac: a cardiac veterinarian specialist uses an echocardiogram to listen for abnormalities in the specific valves in the heart. This test is quick and easy for dogs and owner, but is very expensive.

Eyes: formerly known as CERF testing and now considered under the OFA umbrella, the eyes are dilated and examined under magnification by a specialist for abnormalities. The genetic test JHC is for Juvenile Hereditary Cataracts, performed using a cheek swab mailed to a lab.

Spine: there is currently a very limited database for spines, but it is nice to examine and record them regardless, since spinal issues are common in Frenchies. This is due to their being a dwarf breed, which involves a compact build (current trend even more so), shortened legs, and shortened spine AKA corkscrew tails.

BOAS: this stands for Brachecephalic Obstructed Airway Syndrome. Basically, the sounds and symptoms generally associated with any snub nosed breed, but to the extent that it can cause them functional issues. These can include sensitivity to heat, snorting, snoring, loud panting, and regurgitating foam or food when excited or heated. It is a very difficult balance to make a Frenchy of good type, who also has none of these issues. The issue is caused by a combination of tight nares (nostrils), shortened snout, long soft palate, and of course a narrowed trachea, extra compact build, reflux, allergies and spinal issues can all compound the problem. Besides breeder complacency, one setback to improving this is that historically there has been no grading system for this combination of attributes....until 2018, when Cambridge began testing brachecephalic breeds with a plethysmographs and assigning a score. Since most veterinarians, in any country, do not have this equipment nor have the demand to invest in it, the researchers simultaneously created a functional scoring system, that while somewhat more subjective, is simple, quick, and inexpensive to perform for any vet. My vet graciously agreed to perform this test on my dogs. You can see the actual Cambridge system here:

Understanding Health
Understanding Health
Velvet's Results
Maisy's Results
Ghost's Results