[Edited:] Voltaire meant it the way you have interpreted it: you shouldn't always be looking for something better if you have something good; it's hard enough to keep what you have.
Here are the relevant lines from the poem, with my translation à l'improviste:
Dans ses écrits, un sage Italien [In
his writings, an Italian sage]
Dit que le mieux est l’ennemi du bien
; [Says that the better is the enemy
of the good;]
Non qu’on ne puisse augmenter en
prudence, [Not that we cannot grow in
En bonté d’âme, en talents, en science
; [In the goodness of our soul, in talents,
Cherchons le mieux sur ces
chapitres-là ; [We should search the
better in those fields;]
Partout ailleurs évitons la chimère.
[Everywhere else, we should avoid that chimera.]
Dans son état, heureux qui peut se
plaire, [In his state, that man is
happy who is content with
Vivre à sa place, et garder ce qu’il a
! [Knows his place (live at his place), and protects what he
Voltaire based this on the Italian proverb, Il meglio è l’inimico del bene, which means exactly the same. The origin of the proverb appears to be unknown.
He uses the Italian phrase himself in his Art dramatique. First he describes how the work of Lulli is misinterpreted by a certain encyclopaedia of art; then he "proves" how wrong it is (if I understand the text correctly), and ends with the proverb. I don't think it could be read otherwise than Lulli being the good, and the all-too artificial encyclopaedia being the "better".
Incidentally, I ask, how did Voltaire learn this proverb? He must have heard someone else use it. And either that person must have used it the same way Voltaire uses it, or Voltaire must have misunderstood. Is the latter likely? I imagine this person used it in a context that let Voltaire interpret it this way; it seems possible, but unlikely, that he misinterpreted it.
Suppose there were two women, Cleopatra and Xanthippe. Suppose Cleopatra were the enemy of Xanthippe. Who would you say was more aggressive? I say we know that Cleopatra is probably aggressive, but Xanthippe might be either aggressive or merely fearful of Cleopatra. Being someone's enemy is often reciprocal, but not necessarily so. In any case, if one party is called an "enemy", emphasis lies on that party's ill will.
Analogously, the better harms the good, but we aren't told whether the good harms the better as well. It seems clear that it is the harmful effect of the better that has focus, not the other way around. Moreover, the main statement is dans son état, heureux qui peut se plaire; the phrase non qu'on ne puisse augmenter en prudence etc. ("not that...") is an exception he makes. The main statement is reinforced by the evocative word chimère. What comes before non que... belongs to the main statement.
Any text can be interpreted in various ways, many of which would be the opposite of what the author meant. If an author inspires you to contemplate something you know he didn't intend, that is of course fine and well—as long as you don't try and read it into his other lines. We are not Voltaire's servants: if we should like the wordplay of this expression's meaning "the good is the enemy of the better", we are free to do so.