Joep, the design requirements of any specific French Drain system is dependant upon many parameters, such as the nature of water to be drained (groundwater or storm water), peak flow rates, infiltrative rates of the soil in the area to be drained, and several other variables. My recommedation is to contract with a professional to design the system for the specific needs of this application.
If you desire to “go it alone”, however, there are some gravelless French Drain alternatives on the market that you may wish to investigate.
Advanced Drainage Systems, Inc.(ADS) makes a material called Advan-EDGE, and it is an excellent alternative which allows flexibility in the design of the system, and is easy to install. You can view this material at the ADS website: http://www.ads-pipe.com
Another gravelless alternative drain material is called DrainCore2, which is manufactured by Invisible Structures, Inc.. This material can be used in various drainage applications where the Advan-EDGE is not appropriate. The website address for Invisible Structures is: http://www.invisiblestructures.com