What the contractor claims (if I understand everything correctly) will be true AS LONG AS the system is new and clean. The problem will come after a while as it begins to silt up in the low spots and if roots penetrate into any of the pipe joints. Roots will love the combination of soggy low spots and humid high spots. Water is slowed if it must push other water up a hill in order to move it out of the way. That's when suspended solids drop out of the water and drop to the bottom of the pipe. All storm water is dirty so, over time, those solids will build up and become a fine home for invading roots. Built like a roller coaster, the system will NOT be self cleaning. Check the terms of your contract. Are there specifications that he must work to? This would not be considered standard or good workmanship. You do not say if the contractor has been paid. Find a way to make him re-do this work.

As a general bit of advice to anyone having in-ground work done, people should find a way to inspect things before they are back-filled and made hidden. And, of course, they should have some reasonable written specifications that the contractor must adhere to.

Thanks for the comments Yardvaark.

There was not a written contract, only a verbal agreement. He has not been paid for any of the work. He refuses to correct the problem because it would require digging and pulling out/adjusting the entire system. They insist that their system is in working order and will do its intended job.

I was actually on-site for a good bit of the work. I even went out and checked the pipe with a level (they were not happy that I was checking their work) and found the pipe to be running uphill. Their response was "it's not finished.. it will run downhill... don't worry".

I should also mention:

They hit the gas line at the street with their trencher. The fire department and gas company were out here all day. I had to miss a day of work. The utility company tore up my yard and the neighbors yard to fix the line.

Then, later, the crew hit the water line while trenching.

The yard had been marked by the city days before.

There is no explanation for this incompetence.

The only time corrugated drain pipe should be used is to circumnavigate around barrier elements or if an angle is required - and when used it should always maintain the adequate prescribed fall of grade.
On straight runs rigid pipe should always be used, exactly for the reason you are currently exploring.

This is the beauty of having a professional designed detailed drainage system, whether it was designed by a soils engineer, a civil engineer, a drainagae engineer or a landscape architect . You will pay for the professional services and it will be engineered correctly and they hold liability for the system.
The documents are a binding agreement when your contractor correctly installs the job .
The design documents can also be sent out to several contractors for competitive bidding and you will be assured that each bid is an 'apple to apples' cost estimate because all the spec's ( with the exception to found buried elements) will be documented.

In the long run, it is almost always cost effective to have a professional create a plan for a contractor to follow , - especially if you are working on a verbal agreement with a contractor ( which is never a good idea).

There is a book that contractors have that contains ready BS answers to customer's complaints and concerns. One of those answers is, "It's only temporary. We're not finished." Another is, "We're going to get to that next." There is an answer for nearly any problem that crops up and they are BS because the problems remain unaddressed to the end. Their drainage system may be in working order today, but it will not last.

This is now a dilemma and I feel for you as it's an awkward and uncomfortable position to be in. It's good that you haven't paid the contractor yet as that might be the only accessible leverage that you have at your immediate disposal for getting any satisfaction on the project. Unfortunately, the situation is moving into the legal realm and what you can or can't do I can't predict. You need the guidance of an attorney. You might need to put serious pressure on the contractor (like demanding the job must be done correctly before any payment will be made.) Where it goes no one can tell, but I'd be making notes about what happened so that you have a record if you should need it.

Look on the bright side; in LA you probably don't have a basement that now leaks from putting in an inappropriate french drain.

The term french drain commonly refers to a perforated pipe embedded in gravel. The fact that it took so long for water to start running in the system makes that the likely case as all the gravel has to fill up first.

By installing surface inlets (catch basins), there is the implication that the problem was one of surface water. French drains are an inappropriate fix for unwanted surface water. Inlets and solid pipe can handle small amounts of surface water but it's better in most cases to regrade for water flow across the surface to the discharge point.

It's unfortunate that a lot of homeowners think a french drain is the one-size-fits-all solution to a drainage problem. It sure makes it easy for a contractor to make a quick sale on a profitable job. Some contractors know it's not the right thing to do, others don't. Most don't care one way or the other if there is a profit to be made. How can it be wrong if that's what the customer wants.

You make some good points pls8xx, as did deviant. I wish there was a good way for people to see such comments before they hire a contractor to perform work--especially pertaining to drainage--that is only visible in the contractor's head.