Hi skyserfin,
The polyfoam in your support layer is “stiffer” and less flexible than latex so normally a platform foundation with solid non flexing slats with 3.5" gaps would be fine (assuming it is strong enough for your mattress and the people sleeping on it and also has good center support to the floor).
Based on the picture though … your frame appears to be the same as the Handy Living bedframe/foundation. A forum search on “Handy Living” (you can just click this) will bring up more posts about it (including the first half of post #11 here) but overall it wouldn’t be my first choice because it doesn’t appear to be the strongest choice and the flexible slats are a little further apart than I would be completely comfortable with.
Phoenix