French drains around the perimeter help, but you're literally fighting water from all directions... including directly underneath.
Have a perimeter French drain but a crack in the slab? Enjoy watching water bubble up from that crack once things get saturated.
There isn't a "perimeter" per se, because water is literally coming from depth (in most locals / soil types).
So drain/pump just creates drier 3d soil areas. Whether that's enough to attract all the surrounding water (at a high enough rate) that would otherwise be infiltrating depends on soil permeability (e.g. sandy or clay?).
A lot of the "handyman"-type "dry basement" shops have no idea about any of this, toss a generic solution in there, and then blame the gods if it doesn't work (and they've billed for time-consuming and expensive excavation).
It gets dicey applying internal barriers, because one needs to be thoughtful about making sure there's a place for water to go when it's actually too much (you don't want an internal barrier to be a dam holding back all the pressure), but it can be an option.
They sell them in membrane form or paint-type form.
I'm assuming it's a fully-enclosed basement? I.e. no walk-out side?
The best you can likely do is waterproofing the basement walls + pumping out from inside or an inside-perimeter drain. But that's only racing pump_out_flow > seep_in_flow.
And that's a bad game to be in, because water under pressure (which it will be a story below ground) finds a way.
I'd make the basement flood tolerant (limit mold-hosting materials and places water can be trapped) + pump it out quickly after it floods + buy a dehumidifier, and accept it's going to happen.