I bet once you fill it with soil flooding like that will be less of a problem, but if you wanted better drainage a French drain would definitely do the trick.

Before I'd even consider putting in a French drain, I'd consider a couple of other options. First, do you have a rain gutter system on the rest of the house that carries the rooftop water away to one side of the house or the other to come down a downspout? If so, I wonder why this area was not included. And, if not, maybe that is an option---to just divert the water to go elsewhere so it isn't trapped within that bed surrounded by concrete. Secondly, keep in mind that over just the last 60 days, most of Oklahoma has had around 200% of our usual average rainfall and that is on top of having record rainfall for 6-8 months now across most of the state, so we're all seeing more standing water than usual. Most years are not like this. Third, check out the soil in that flower bed and see how it drains. The issue might not be how much water is sitting there---it might be that the soil is compacted and/or is slow-draining clay and drains poorly so the water sits on the surface for longer than you'd like. I'd work on adding some organic matter to that soil to see if I could improve drainage. In order to keep the soil grade below the concrete, you might need to dig out some of the existing soil and just replace it with a better growing medium that drains a bit better. If you're getting rain every other day or so like many of us here in OK have been, I'd watch it for a few more days and see how quickly that area drains if we ever manage to go for 4 or 5 days straight without rainfall. If you can get the drainage there to improve just by correcting the soil, then whatever plants you choose to put there should do fine in the future.

That will be so fun to fill with plants and flowers! All of my thoughts on your situation were already covered by Dawn.