Why can't you rhyme 'orange', when French poets happily rhyme a word with itself?

Because every language gets to write its own rule for what counts as a rhyme. In English, two words rhyme if their final stressed vowel and all the sounds after it are identical. Identical rhymes are considered less than perfect in English poetry, so flour and flower would seem weak. French poets take the opposite view: identical rhymes, in which even the consonants before the final vowel match, are common, and the homophones doigt and doit make a perfectly acceptable rhyme. To an English ear, it often sounds like a very weak rhyme. In French it can even be prized, as rime riche.

The rules are not only about taste. Some English words, such as orange and silver, are commonly regarded as having no rhyme at all. A clever writer can sidestep this by rhyming orange obliquely with phrases like door hinge or more range, or with the Welsh hill name Blorenge. Other languages set different tests. Spanish allows assonant rhyme, where only the vowels at the end are identical, as in zapato and brazo. Chinese rhymes often include tone. And because of the structure of Italian, a rhyme scheme such as the Petrarchan sonnet's is more easily fulfilled in Italian than in English.

Why bother? Rhyme is partly enjoyed simply as a pleasant repeating pattern, it is a powerful mnemonic device, and it marks off the ends of lines for the listener. John Milton, in the preface to Paradise Lost, called rhyme the invention of a barbarous age.