"We will beat our opponent not by being stronger than them, but by being cleverer than them."
Nous allons battre notre adversaire pas en étant plus forts qu'eux, mais en étant plus intelligents qu'eux.
Is "pas" the correct translation of "not" here? Or should it be "ne pas" or "non"?
Before I specifically answer your question, I need to make a little summary, as this is one of the very idiosyncratic points of French grammar.
The "mystery" of French negatives
The trick is to remember that the words "pas, plus, jamais" were not created negatives. They have a positive meaning.
pas => little (no longer used in this way)
plus => more
jamais => ever
Hence:
Plus il boit, moins il pense. => The more he drinks, the less he thinks.
Si jamais tu le vois,... => If you ever meet him,...
As tu jamais vu cela? => Have you ever seen that?
The only proper negative in French is "ne".
Hence:
Ne... pas => "not a little" => not
Ne... plus => "not more" => no more (quantity), no longer (time)
Ne... jamais => "not ever" => never
It is very simple, really.
What makes it confusing, is that modern usage tends to forget it:
Vas-tu accepter? -- Jamais! Plutôt mourir!
Non, mais j'ai jamais vu ça!
So, in essence, the meaning of the word "jamais" has been completely reversed. It is like if you said "ever", instead of "n-ever"! Only the context allows you to tell which is which.
The recommendation here would be, in written language, to strictly respect the standard construction.
Conclusion: There could be argument on whether your version is acceptable or not (because French grammarians have thrown their arms up in despair about this); but the standard, unambiguous version should be:
Nous allons battre notre adversaire, non pas en étant...
Singular/Plural
Ah, and another little detail: the English facility of having a singular noun used as a plural is frowned upon in French.
So you would have to say either:
Nous allons battre notre adversaire, non pas en étant plus forts que lui, mais en étant plus intelligents.
Or:
Nous allons battre nos adversaires, non pas en étant plus forts qu'eux, mais en étant plus intelligents.
I also removed "que lui/qu'eux", as this was redundant (but at this point, it becomes a matter of opinion).
Your question was very interesting, so it deserved a long answer.
