For better or worse, I have a lot of projects where I have done this, usually without the need for a drainage engineer, because, as Brad Klein once wrote, I am a drainage nerd.....
But, its pretty simple conceptually......raise all fairways to a minimum 2, 5 or 10 year flood elevation, leaving roughs low. How much is a site specific question. Of course, you need to dig some lakes and make sure you have the compensatory storage volume in the free board, not always an easy task, and sometimes leading to more water holes than you want. Greens and tees get raised to 25, 50 or 100 as feasible.
Then, re-grade most areas to have minimum 3-4% slope so the water moves faster to drain outlets when it can. Oversize catch basins for silt intrusion, expect to clean them out (also, make at least some big enough for humans to get in for maintenance)
I rarely use french drains in similar applications, because the silt or each flood tends to weaken their function.
Hopefully, it can be done with a gravity system, but sometimes, as noted, pumps are a nice addition.
Like I say, I have done this so often, I can do it in my sleep. Well almost......Years ago here, I was accused of taking swipes at Gil and Geoff for not raising the fairways at Rustic Canyon. Geoff said regulations prevented it, and I agree (as per above) that they surely at least limited it. But, he also mentioned that they wanted to preserve "micro contours" so I could never be sure of what the whole deal was, nor was I going to research it.
My only point was that to nerds like me, the idea of NOT raising and grading fairways to limit flood damage and speed drainage a pretty foreign concept.......and that sometimes, basic approaches other than minimalism were required.