Should I attach underground drain pipes to the existing downpipes and redirect away from the house, or should I also include a French drain to avoid future digging?

Hey everyone,
I shared a photo of the house earlier and got some advice to add a French drain, which I’m planning to do. I sketched out a rough idea of what I have in mind and would love to hear what you think.
The blue dots in the drawing represent the existing gutter downpipes, and the red lines show where I’m thinking of putting the underground drain pipes.
I’m torn between just connecting the underground pipes to the downpipes and re-routing them away from the house while fixing the grade, or if I should go all out and include a French drain too. I really don’t want to have to dig under the sidewalk again later on if I can avoid it.
Thanks in advance for your thoughts and feedback!