Manouche-technique
I use the term 'manouche' to describe this special playing style. Because if I'd say 'gypsy', it would include the spanish gypsies (called gitans). But they play flamenco, and this technique is very different. What's typical for all gypsy-guitarists (gitans, manouche, sinti), is a hard and well defined precise attack. And the fact, that guitarists play always seated.
The strings we use on these guitars are always "ARGENTINE" by Savarez. (gauge 011 to 046).
Whereby the high strings E and B are plain steel, while the four lower strings are silver-roundwound with a nylon core.
It's the technique of the right hand
(here I'm talking about lead and melody playing!)
It's certainly the right hand technique that makes the guitar sound different. With it goes the use of a stiff and thick plectrum. They are mostly made of horn, bone, ebony or 'delrain' (see article about Dugain picks).
Gypsy players have a loud and hard attack. This is achieved by a free moving hand (same as when you strumming rhythm). Because the right hand fingers don't rest on the top or the bridge of the guitar, the force and the swing of the attack of each note comes out of the entire forearm. The fist acts as an extra-whip and so the whole movement is a loose and free picking of the string!
In the beginning it will be difficult to land always on the right string, because there's no more pivot point on the guitar with the hand. This IS very important, because it's the only way to get a real hard and loud attack. (Also for one string rolls and other gimmicks).
As I said, we're talking here about lead/melody playing. But for rhythm/chords playing, the technique and hand position is the same. That is very useful to switch between lead and chords at any time.
Listen to Django, even on slow and quiet ballads you can almost physically feel the strenght and clearly defined force in every single note he plays!
Illustrations
1) To give sense to this change of hand-positioning and picking technique you must use one of those thick DUGAIN-style picks (mostly made of horn, bone, ebony, even stone). I craft mine out of coconut-shell.
Django himself used to carve his picks out of horn- or tortoise-shell-combs!
2) All the fingers of the right hand are curled inside, almost a fist, but still relaxed. The right hand is not parallel to the top but is curved and points toward the strings. The pick of course between index and thumb.

3) The point is that no part, no finger of the right hand touches the guitar. You don't have no anchor or pivot anymore on the bridge or the top of the guitar.
Mostly we touch the top with the pinky or ringfinger. Or the palm of the hand rests on the bridge. Thats over! Forget it! Forbidden!
The only part that rests on the guitar is the inner part of the elbow. And there's also a slight position changing in general for the right arm. But you can only get that by exploring exactly the illustrations.

COMMENTS AND QUESTIONS
Please go to my guitar-blog to post any comments or questions. http://twohands-guitar.blogspot.com
Thank you