Thank you in advance for the advice. My neighbour raised the level of their back yard by adding soil and consequently, my back yard floods with every rainfall as in photo. I don't want to raise the level of my yard by adding soil and regrading, but am looking for solutions. I thought of a french drain, but think it would be pretty large. I will likely proceed with a french drain unless there are other options. Looking forward to other options, and if none, any advice on the french drain solution.
It seems like you're already onto the best option. Here's an article with some additions:
info - sorry you're having this problem: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/yard-drainage-problems.htm