According to research and our experiences, Frenchies are very moderate barkers and tend to bark only when they feel something is really worth getting excited over. They are certainly not excessive barkers, such as our Yorkies were.
We have observed that there is also a big difference between our various Frenchies in this regard. None are excessive barkers, but some bark at things that our other Frenchies will ignore. For example, there are horses on the property immediately adjacent ours. When the horses are near the fence, a couple of our Frenchies will bark at them a few times, just to let them know they are around, I suppose. The rest of our Frenchies will completely ignore them or go to the fence to try to make friends, but not make a peep in the process.
We also had a funny experience a while back when we heard one of our female Frenchies barking in our bathroom. We had thought she might be mute because we could never remember hearing her bark before; but, here she was barking her head off. It turns out that what she was barking at was her reflection in our shower door. The sun light was just right so she could clearly see herself and she knew there was a dog in her domain that she did not recognize. We laughed like crazy. When we opened the shower door and showed her there was no one there, she finally calmed down.