Shaking or trembling could be due to hypoglycemia, liver shunt, or a neurologic response such as a seizure. Trembling can also be a sign of pain, stress and cold.
Hypoglycemia is low blood sugar and frequently causing trembling in small breeds. Feeding your dog smaller meals more frequently can help. If you suspect your dog is having low blood sugar you can put a drop of pancake syrup on your dog's tongue which should raise the level.
A liver shunt is usually a genetic condition. It is a condition where instead of the blood going through the liver and being cleansed, part of the blood is diverted around the liver resulting in a toxic buildup in the blood. You can read about these here: http://www.malteseonly.com/shunt2.html
Seizures can manifest as trembling and a dog may not lose conscienceness. You can read more about seizures here: http://www.marvistavet.com/html/body_seizure_disorder.html
Swaying could also be a part of a neurological response or be related to disorientation or even an ear infection which is affecting the vestibular system and pain. Dogs with ear infections can have problems with balance, swaying, and pain. So this is a possibility.
French bulldogs are also prone to a few spinal issues such as disc issues and hemivertebra. In many cases hemivertebra is not a problem unless there is disc compression present and many dogs are diagnosed after being examined for another cause. You can read about it here:
Your breed is prone to disc issues. An intervertebral disc that has slipped or ruptured up into the spinal canal causes inflammation of the spinal cord, which in severe cases causes paralyses of the rear legs. It can cause pain, loss of coordination and trembling from pain and stress. You can read about this here:
If you feel this might be the cause, buffered aspirin can be given to a dog with a dosage of up to 5-10 mg per pound every 12 hours for pain. Keep in mind that a dog's body does not metabolize aspirin in the same way as a human and thus should not be given more than a day or two without contacting your Vet. Read side effects and precautions here.
If your dog shows no improvement, I'd have her seen by your vet.