The good news is that the french drain is definitely working. This is the sump pit which is a garbage can buried in the ground with the french drain perforated pipe flowing into it.
I did have some concerns that perhaps the french drain wasn't draining into the sump pit and that the reason the french has worked thus far, is just because there is now a gravel trough that runs the length of the yard and that trough was holding the rain runoff. Now, it's fairly obvious that the drain is working well.
The bad news is that because the sump pit is fully filled, water isn't draining in the trouble areas of the yard so that this is happening:
Rachel's Grandpa had given us a sump pump and it worked, but not great when I first tried it. It seemed that perhaps the 1/3 horsepower wasn't enough to push water through the 4 foot hose I had connected to it. This morning, I hooked the pump up to a 50 foot hose with no expectations. I need to pump the water out to the front yard so that it can drain into the gutter.
Luckily, the sump pump worked! Perhaps it was the hose I was using before? No idea. Hopefully, now that I am pumping the water out of the sump pit, the standing water in the yard will drain into it and we'll have a dry yard again.