Suggestions for Connecting Filter Backwash Drain to French Drain?

I've created a pump house to house all of the filtration equipment for our well.
All of the downspouts are connected to a French drain. I wanted to be able to connect all of the Filter Backwash Drain lines to the French Drain system.
I figured while I'm at it I'd connect the booster pump top the French Drain too in case I want to Empty the 5000 Gallon Storage tank, I could use the booster pump and just pump it into the French drain system.
I was thinking that just outside the Pump house I would have a piece of 3" Flex Drain pipe (like for the Downspout) and just drop an 1.25" pipe a foot or so down the 3" drain pipe. Then on the inside just hook everything up to the 1.25" line. With the appropriate check valves and valves to prevent water from going where it shouldn't go.
Would I need a P-Trap in the Pump house? There really isn't any sewer gases... though not sure what's in a French drain.
Any Suggestions on how to make this work?
Thanks, Scott<-

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