The simple answer is that the Luftwaffe wouldn't (unfortunately IMHO) buy the Mirage, because they needed a tactical nuclear bomber and the French refused to provide the Germans with the necessary technical information to do this.
So, we're probably looking at the Germans buying an alternative American design - although it would be hard to find one less suited to their needs than what they actually bought.
In this early post you say, they wanted a "tactical nuke bomber" and that is exactly what the Republic F-105 "Thunderchief" aka "Thud" was designed originally to do.
But then farther down you say, what they really wanted was one airplane that could not only serve as a tactical nuclear strike bomber but also as a "STOL interceptor," whatever exactly you mean by that.
As an interceptor the Thud would not be very impressive I guess and it certainly wasn't "STOL." But what other airplane of the early 1960s could meet all these qualifications? I think it's a little odd to imagine the need to have one airframe carry out both those tasks.
If you want a plane that can deliver a whole lot of ordinance through a very tenaciously defended airspace and then make it home again most of the time, supersonic, the F-105 could do it. Could any plane, made in any country, do that and also qualify as "STOL" and have the rapid climb and speed and yet maneuverability one would hope for in an interceptor?
I'm not trying to push any US design designated an "interceptor" because defending CON-US and defending Western Europe, front-line West Germany especially, are very very different missions. Before throwing in the towel on interceptors completely on the reasoning that "The ICBM will always get through anyway, so meh..." American designers were feeling a need for speed above all else--hence several Mach 3+ designs, including a version of Lockheed's A-12 (F-12) and North American's F-108 (basically a scaled-down version of the Valkyrie B-70 supersonic bomber, with very similar planform and the same engine). The idea was to zoom out to detected incoming bandits and engage them as far from their North American targets as possible. The last model actually deployed with the interception mission mainly in mind was the F-106, and had the superfast giants been actually deployed for a while the Delta Dart would clearly be an intermediate point in an evolving tradition of "go fast and screw everything else; maneuvering is for wimps..." Though I do think the -106's delta planform did also enable it to maneuver rather better at low speeds than most Century series fighters. Nothing in the Century series could be called "STOL" (except the abortive F-109 which was to have been VTOL!

) but again I daresay the delta wing did on the whole make takeoff and landing notably brisker.
The -106 was my father's favorite by far. But the only time he ever fought in an actual war, 100 missions bombing North Vietnam, it was an F-105 he flew.
If the French won't sell an appropriate Mirage, would the Germans consider looking northward to Sweden? It's a decade too early for the Viggen but the
Draken was just rolled out in 1960. Unfortunately the Danish version that was heavy enough to carry Bullpup air-to-surface missiles would presumably be a late evolution; Bullpups themselves only developed a nuclear version late and that might have been too heavy for the Danish Drakens for all I know! So no, it wouldn't serve in a tactical nuclear strike role I guess. But if you want a STOL interceptor designed for European fighting conditions (ie scramble in just minutes, get airborne, climb like a sonovabitch and engage immediately because the enemy is based just minutes over the border!

) I don't know of anything better; the thing could land on highways! (Well, suitably prepared stretches anyway).
As I say I'm very puzzled that any air force would look for nuclear strike capability and a scrappy STOL dogfighter and interceptor all in the same airplane. The economy of making one type of airplane serve all needs is plain enough, but wasn't that a rather insane notion?
And the crazier thing is of course accepting F-104, not for the interceptor/fighter mission (that is what Lockheed had in mind designing the thing--according to American expectations of plenty of long runways and the need for speed to get to the battle) but for nuclear strike, forsooth!

"Hey Tinkerbelle, you man the cannon!"
Bribery was apparently the only explanation.