Your crankset looks like it is not ramped and pinned, that makes it a bit less smooth. (My older bikes built in the 1970s and 1960s do not shift very smooth either.) In my case, the 24t granny chainring is not matched to the 42 ring ramps and pins, as the 24t is an aftermarket one, so that hinders shifting somewhat. Also, you can't really expect a jump from 24t up to 42t to be very smooth, as that is a big jump. It actually looks like a big jump in the photo.

I think a different derailleur may not help, so I would not bother trying to upgrade that. But a crankset that has ramped and pinned chainrings might be smoother. If it was me I would not upgrade. But, I have never ridden a tandem. Your riding partner might not agree with me, they might want smoother shifting.

I do not know if an older crankset that was designed for use with a 5 or 6 speed freewheel will work smoothly with an 8 speed chain, that may be another issue. Since I have never tried this combination, I am quite ignorant of potential incompatibility with the narrow chain.

My preference for the older Suntours are specific to the high normal derailleurs. Only some of theirs were high normal. With my bar end shifters, pushing both shifters all the way forward puts me in the highest gear. I am not pushing on one shifter and pulling on the other to upshift. I found a local store that had some new-old-stock ones, I bought a lifetime supply of them. From your photos, I think yours is not high normal.

The bike shop I worked in carried Gitanes, but that was many many years ago. I assumed an old Gitane had Simplex equipment, I am surprised you have Suntour.