As others have implied, there are at least three or more ways of dealing with the problem.
1. landscaping to eliminate the low spot, no more mud
2. drain the water from the low spot by allowing a quick easy path with the french drain
3. get rid of the most of the soil that makes mud, replacing it with gravel. They make plastic grass saver tiles that provide firm footing, and allow grass to grow through it. Mostly used for vehicle traffic over grass, but could be used in this case.
4. build a bridge. It doesn't even have to be exposed. dig out two trenches to lay long 4x4's in, and cover with the landscape pavers. (the big ones... 24" square) Maybe something like
StabilGrid.
Getting the water to flow is the best longterm solution. Either the french drain, or the landscaping to eliminate the lowspot. The french drain doesn't even have to be visible. Upslope side has gravel to allow good drainage, and the downslope side has another gravel filled hole to allow the water a place to go to, until it soaks away down hill.
Michael