I would have to argue that there is actually very little connection here, and that the question's implication that there is one reflects a romantic attitude that makes such a misapprehension admirable, but still idealistic and probably incorrect. Let me explain: In The Little Prince, the Fox explains to the Little Prince that "It is only with the heart that one can see rightly; what is essential is invisible to the eye." This is indeed a lovely and profound thought, and is a favorite quotation of many romantic people. However, if we read The Little Prince, we learn that love is associated with the idea of taming, that when we tame someone we "establish ties" such that "if you tame me, then we shall need each other. To me, you will be unique in all the world. To you, I shall be unique in all the world . . ." (66). We also learn that this process takes time: "You must be very patient. . . . First you will sit down at a little distance from me. . . . But you will sit a little closer to me, every day . . . ." When the Fox tells the Little Prince at their final meeting that what is essential is invisible to the eye, he adds, "It is the time you have wasted for your rose that makes your rose so important." And "You become responsible, forever, for what you have tamed. You are responsible for your rose . . . ." (71) The point I am trying to make is that this is all a slow and gradual process: it is not "love at first sight."
By contrast, Romeo and Juliet is all about speed. Everything happens much too fast. They meet, marry, Romeo is exiled, Juliet feigns death, Romeo kills himself, Juliet kills herself--all with stunning speed. And Juliet knows this even before it happens! She tells Romeo during the famous Act II, scene 2 balcony scene:
Well, do not swear. Although I joy in thee,
I have no joy of this contract to-night,
It is too rash, too unadvis'd, too sudden,
Too like the lightning, which doth cease to be
Ere one can say it lightens. (II.ii.115-120)
Tragically, which is perhaps appropriate for a "tragedy," Juliet then contradicts her own wisdom only 23 lines later:
If that thy bent of love be honorable, thy purpose marriage, send me word to-morrow...
Where and what time thou wilt perform the rite, and all my fortunes at thy foot I'll lay, and follow thee my lord throughout the world. (143)
So, a huge part of the tragic action in Romeo and Juliet relies upon everything happening too quickly.
Now, if one chooses to believe in love at first sight, and to believe, correctly in my estimation, that Romeo and Juliet each saw something essential with their hearts in the other, then perhaps one can twist the play to illustrate the point of the Fox from The Little Prince, but I believe that Shakespeare's message is that if you don't want your children to end up dead, teach them that things take time! I believe the Fox would concur.