Keep in mind that backyard access usually means children and their friends will be going back and forth tracking in mud, carrying frogs, etc. Pets will be let in and out, and the gardener in the family will be coming and going with their latest harvest of zucchini and put the door somewhere the high traffic makes sense. Kitchen floors are easier in general to clean, but if the table is in the way it becomes the landing zone for the garden bounty, gloves, hats, pruning tools, motor oil for the lawn mower, and anything else someone is taking out or bringing in.

Good point on the floors; however we'll have hardwood throughout kitchen and family, so that would be a neutral.

So if floors are a neutral, I'd also wonder if the traffic would potentially cause other problems - ie does the person who cooks worry about the traffic coming and going or accidents happening (that boiling spagetti pot getting knocked off the stove by boisterous young ones running and not paying attention)? Does the location make the door more secure or less if someone is casing your home to rob you? Is one location easy for neighbors to see and one hidden from view where someone could break in? What is the view like, since you mention French doors, do you want the extra sunlight and the view in the kitchen or in the living area? Will one location overlook the garbage cans and the other look at the beautiful old oak?

As far as kitchen traffic, that's also probably a neutral as the stove is far enough away. Both doors would face a private backyard with a nice view (lake in the background). French doors in the family room would really make the most of the view though as they are more centrally located. If we put the door in the kitchen, we would just have a large (7') window in the family room looking into the backyard.

Think about what you would use the backyard for. If you plan to dine or BBQ in the backyard, it would probably be more convenient to have access through the kitchen. If the French door swing is really a big issue, you can have the doors swing out. Out swing french doors are not that usual, but they work just as well and they don't change the look.

I agree that you should consider access from both rooms........
You can always choose to keep the French doors shut with a chair in front of them if you don't use them very often. It will look lovely.

When you do have a back yard BBQ or a party with people it will be nice to open up both doors.

Thank you for the suggestions! I really like the idea of having two sets of French doors in the kitchen and in the family room. Now I just need to get my husband on board with that!

We just bought a house with both in it . While it looks good but I wouldn’t want people from backyard coming straight to my family room
Where we would have a carpet n stuff. So going to close that and make it a big picture window instead .