The way people use the term "French drain" today makes it not any different than any underground drain. An underground drain pipe is useful when you must translocate water from one low point of the yard to an even lower point elsewhere in the yard and have to pass through a higher elevation area along the way. But if all along the route, at the surface, you need to be collecting and translocating water, then an underground drain is not helpful. What you need is surface drainage: slope, swale and/or flume. The exit point in your yard for drainage water is the ditch. And the water needs to get to it, along any point, using one of those 3 devices. It's not necessary to worry about every square inch of the yard. Out in the wooded portion, if the yard is juicy and sloppy for a day or two after the rain, does it really make a material difference? Probably not. What's likely to matter most is the area all around the house, the drive and the storage building and access to it. Mainly, you need to be evaluating how you can get water from the left side of your yard to the right side, where the ditch is. It looks like the biggest problem you're showing us is standing water in front of the storage building. It would help if that building was raised up a few, like 6 inches. If it's sitting on the ground, you could raise the grade with soil, gravel or by pouring a concrete slab (if the building needed a solid floor.) Also, the approach ground in front of the storage building needs to be raised, with a slight cross-slope tilted rightward. From that point on, you could create a swale between the building and the trees and the trees and fence. The bottom of the swale would be continuously gradually descending in elevation as it travels toward the ditch ... roughly about 2 1/2" to 3" per every ten feet. The swale profile can be gentle. Establish the bottom center of it first (like a channel) and then carve out the sides to make it blend more gently into the surrounding grade. If the space is really tight between the trees and fence, then you may need a flume ... a concrete lined channel. Think of it as a splash block (like would be below a downspout) but that runs the entire length of the channel. The reason it's concrete because water is moving faster in it that it would be swale, so it can erode the ground. I looked on Youtube but couldn't find any videos about making a drainage flume. Usually, they are just hand plaster in by some grandpa. A poor man's flume could be made by lining a channel with roofing shingles oriented the same way they would shed water on a roof.

Good morning Yardvaark! Thanks for getting back to me. I looked up these terms. I am glad I don't need a French drain. I am generally following what you are saying, just some additional questions:

1. What would I use to make swales, are we talking a bobcat?
2. Would gravel help with any of this re dry creek bed, or gravel walkway in front of the shed?
3. Who do I call to add height to the shed?
4. Am I thinking right about a future retaining wall on the right to keep dirt from spilling into the ditch?
5. I will be eliminating trees bit by bit. What do I do to make sure water does not pool afterward?
   Thanks for you help and feedback!

1. A shovel, hard rake. Or a Bobcat & skilled operator if it fits. (I can't see how much space is at the back.
2. No. Gravel will not help it drain. It's only a way of protecting soil from erosion if groundcover plants can't grow and withstand water forces. But I think they can.
3. A handyman can raise the shed higher.
4. Protecting the ditch with a retaining wall or masonry covering (like it was a flume) would be OK, but check with whoever controls/drainage ways as there could be regulations/permits, etc.
5. fill the hole the tree came out of.

Thank you Yardvaark! This is new to me as you can tell. Good news is it is not as much work as I thought. It may be awhile but I will keep you posted!