Not exactly sure what your trying to do for sure, around here a french drain is a tile trenched in and covered with crushed rock for the water to soak in faster, but for the size of parking lot and the fact its either cement or rock, unless you've got a collection site for water to sit so it can seep in your wasting your time, an intake will take way more water faster than any french drain will, second a 8 inch line is way undersized for what your doing unless you have 2-3 % slope on the line or more, I'd opt for a 10 or even a 12 with several 12 inch intakes on it if you can channel the water to them so they can pool around an intake and run into them. Lastly if you have freezing weather, yes the rock will be frozen when you need it to work in the spring, that's why I don't recommend them at all, because the highest water run off is in the spring when the rock is still frozen and can't soak into the line. I'm not sure how deep your putting this line in the ground or where your outlet will be but with the water volume you'll have it'll create quite a ditch at the outlet end over time. Is the neighbor complaining or the owner of the parking lot? Does the water dam up somewhere along the line where it sits, either at the edge of the property or in the middle somewhere, does the parking lot slope one direction or towards one corner? Pictures are helpful for us to give a good recommendation so we understand and can see what's going on. I'd opt for big tile and several intakes or even more spread out to low lying areas so water can run into them, they never freeze and will take water as fast as the line can take it away, if your going 450 ft we'll need to know what the slope of the ground is now to determine what size line you'll need to help take it away fast enough. Is this in the city? do they have storm sewer's nearby to dump into or can they run a storm sewer up to the property line for you, those are usually big enough to handle this water volume, also where does the proposed outlet end up? Are you going to flood out the next guy down stream beyond the current neighbor?
Around here water can flow downstream as long as it leaves your property the same as mother nature intended it to and there's nothing anybody down stream can do about it, now when you alter where it exits your property or how it exits your property that's where legal problems arise, you can pipe it through a neighbors property and dump it onto the next guy down stream as long as you dump it in the same place it would naturally flow by itself if you didn't use tile, but that depends on the area and state and city laws, so check those all out, sometimes once its put in a tile you need permits to outlet the line even if its in the same place it would flow naturally.
I did something similar to what your wanting to do but for my building site and we used two 10 inch lines with about 5 six inch to 12 inch intakes and put small terraces to collect the water and also put reliefs on the lines to allow excess water and pressure to be relieved, the system works great and water only pools for a few hours after a heavy rain and then it's all gone down and it eliminated all the flooding and washing and soft spots around the buildings where water sat before.
