Frenching, in automotive and custom car lingo, is when you move the headlights (also taillights) farther back into the fender than they are in standard production, giving them sunken look. This is generally done to "old" cars, perhaps pre 1970's, where the circular headlamps would slightly bulge out and were framed by a cuff of chrome or like metal.
Though I won't go into great detail, the process of Frenching headlights is pretty simple; if you plan on using stock headlamps, the standard procedure is taking the flared chrome cuff and flipping it around so that it bulges in and not out. If you're going to use different (read: different sized) lamps, you either can simply inset the lamp with no cuff if the lap is large enough or use a different (usually custom made/ordered) one. The process often involves also moving the headlight mount (called the "cup" or "bucket") as well.
Why would you want to do this? Well, generally because it smooths out the contours of the car -- it removes the chrome abutments that disorder the "flow" of the cars nose, giving it a more liquid look.
As for the name, well, officially is comes from the idea that early French car makers were doing this early in the life of the automobile, but stopped due to designed and cost constraints -- but most sources will concede that that is probably just a fancy story to cover up a slighly seductive etymology; it almost certainly takes its name from a style of kissing where tongues are placed in places other than their owners' mouths, whereupon lies the "inserting" theme.