quel(le)(s) vs qu'elle(s)
Summary
quel/quelle/quels/quelles is an interrogative-exclamative determiner that agrees with the noun it introduces (Quelle heure est-il ? Quel beau jour !); qu'elle(s) is the conjunction/pronoun que elided before elle(s) (je crois qu'elle vient). Both are pronounced /kɛl/. Test: replace the word with qu'il — if the sentence still works grammatically, it's qu'elle; if the word sits directly before a noun and changes form to agree with it, it's quel(le)(s).
Explanation
Quel and qu'elle sound identical (/kɛl/) but belong to entirely different grammatical categories. Quel (feminine quelle, plural quels/quelles) is an interrogative or exclamative determiner: it always accompanies a noun and agrees with it in gender and number, asking "which" or exclaiming "what a...": Quel livre lis-tu ? ("Which book are you reading?"), Quelle heure est-il ? ("What time is it?"), Quel beau jour ! ("What a beautiful day!").
Qu'elle is simply que (the conjunction "that" or the relative/interrogative pronoun) elided to qu' before the subject pronoun elle ("she/it"), or qu'elles before elles ("they," feminine). It appears wherever que would normally introduce a clause whose subject happens to be elle or elles: Je crois qu'elle vient ("I think she's coming"), Le film qu'elle a vu ("The film that she saw").
The substitution test is direct: replace the word with qu'il (masculine equivalent). If the sentence remains grammatical, you are dealing with qu'elle, because il and elle are interchangeable subject pronouns: Je crois qu'elle vient → Je crois qu'il vient works perfectly, confirming qu'elle. If replacing with qu'il produces nonsense because the word is actually agreeing with a following noun, then it is quel(le)(s): Quelle heure est-il ? → "Qu'il heure est-il ?" is meaningless, confirming the determiner quelle.
A second, equally useful cue is what comes right after the word. Quel(le)(s) is always immediately followed by a noun (or occasionally être + noun, as in Quel est ton nom ?), and its ending changes to match that noun's gender and number: quel garçon, quelle fille, quels amis, quelles idées. Qu'elle(s), by contrast, is always immediately followed by a conjugated verb, because elle/elles is the subject of that verb: qu'elle vienne, qu'elles partent.
Do not let the exclamative use of quel mislead you — Quelle surprise ! and Quels progrès ! still follow the same agreement rule, agreeing with surprise (feminine) and progrès (masculine plural) respectively. And in qu'elle, the apostrophe is a strict signal of elision before a vowel; there is never an apostrophe in quel/quelle/quels/quelles, since those words end in a consonant or a full vowel sound already integrated into the spelling.
In short: quel(le)(s) is a determiner that changes its own ending to match a following noun ("which/what a..."); qu'elle(s) is que + elle(s), a conjunction or pronoun before a verb ("that she/they..."). Swap in qu'il to test for qu'elle; check for noun agreement to confirm quel(le)(s).
Examples
Quelle heure est-il ? — What time is it? (quelle: interrogative determiner agreeing with the feminine noun heure.)
Je pense qu'elle a raison. — I think she's right. (qu'elle: que + elle, subject of the verb a; replaceable by qu'il (je pense qu'il a raison).)
Quel beau jour, et j'espère qu'elle viendra ! — What a beautiful day, and I hope she'll come! (Direct contrast: quel (exclamative, agrees with jour) vs qu'elle (que + elle, before viendra).)
Quelles chansons préfère-t-elle, et pourquoi crois-tu qu'elles sont si populaires ? — Which songs does she prefer, and why do you think they're so popular? (quelles (determiner, agrees with chansons) vs qu'elles (que + elles, subject of sont).)
Quel dommage qu'elle ne puisse pas venir ! — What a shame that she can't come! (quel (exclamative, agrees with dommage) then qu'elle (que + elle, subject of puisse).)
Common mistakes
Qu'elle heure est-il ?
Quelle heure est-il ?
the word directly precedes and agrees with the noun heure (feminine), so it must be the interrogative determiner quelle, not qu'elle (que + elle); substituting qu'il here ("Qu'il heure est-il ?") produces nonsense, confirming the determiner is needed.
Related rules
homophonesspellinginterrogativesagreement