If it weren't for the vents and other electrical there by the hutch, I'd advise closing up the two existing doors and putting just one in the center.Doesn't seem feasible though. If both doors go to the same room, I'd close off the small one and move the French doorway to the right, as close to the vents as possible. Can't tell if that will give you the view you want from the kitchen. It looks like the kitchen is to the right, so even that might not work. Are you up to changing electric and ductwork? Hopefully a more qualified technical person can help you out.

How high are your ceilings? Can you raise the french door opening all the way to the ceiling, and widen it all the way to the first vent? I would also close off the small opening, this will make it look less choppy.

How about removing the entire wall?

Is it load bearing? If not, take it all out & if possible raise the height of the "entry". All the electrical and duct work can be rerouted. I just did this in a clients kitchen and the transformation is incredible.