I find the Merriam-Webster Unabridged Dictionary's hypothesis that the second part of the phrase arises from the English 'oop' highly suspect.
Firstly, 'oop' is far from being a Standard English pronunciation, occurring mostly in regional speech in parts of northern England.
Secondly, how is this variant of the standard English term supposed to have got tagged onto the end of the French 'Allez!'?
Thirdly, the circus has at least as long a tradition on the European mainland as it does in England and the USA, implying that French acrobats too needed a term with which to prompt one another to jump (it would be interesting to know if they also habitually use this term).
Fourthly, in French both 'Houp!' and 'Hop'! also exist independently of 'Allez!' as well as in association with it, making it even less likely that the variant English 'oop' has anything whatever to do with the expression 'alley-oop'.
Methinks the lazy do attest too much!
Reply from Erik Kowal ( - England)