The roof coming right down there isn't good without major roofing and structural framing unless you gutter and awning . . a gable awning if the valley that sheds water on the front porch can be directed might work but it will leak and never be rain tight.

Is the interior layout conducive to moving the front door up and adding onto the front gable instead? That would be a lot cheaper, and give you a better look - you probably are already in the process of reviewing what to do with the 70's sliders they put on the front of your cape . . .Using the right side of that gable with something constructed above like this [houzz=]
would give you an overall better result and cost a lot less. Yes, you would want to address the walk by the side of the house and add curvy stairs out front, but the side entrance might become useful to the kitchen / become a dutch door to a mud room . .

You should be able to get the weather protection that you need with several options.

You could build a canoppy

You could install an awning

Or you could build a "Portico" style porch which has a "flat" roof which slopes at 1/2" per foot to drain the water that comes down from the roof onto the driveway.

I don't have an image that fits your exact situation, but I included a few for inspiration.

It would be easy to design a porch - like roof area for your existing front door....

Thanks to those who commented. The "front" door opens into a teeny foyer with a coat closet and then into the living room, so that works well. Yes, I do plan to exchange the sliders for windows... and replace the siding. Hoping to make the house look more craftsman-like.

This is a great op to add a Porte Cochere/entry. Make it simple and modest like the architecture of the house and it will look like it was always there.

Keen planner has some interesting ideas -
Lampert - I saw the valley aiming at 45 degrees right over the front door, and wasn't sure that an awning connected to the fascia or below by bracket would be able to withstand the water coming in - there appears to be no distance between the top of the entry door and the fascia / edge of roof. That was my concern about even a flat slope, but something flat that led to a portico might help you head into cape cod or craftsman territory most easily. .