Bedsted
French citizens can enter the UK using an ID card. UK citizens cannot do this, as the UK does not issue ID cards.
Not Langley
An international driving licence is basically a standardised translation of a driving licence (usually required because the original has a non roman script) and as such is not recognised as a form of ID.
If on doesn't wish to carry a passport (once in a country), a good workaround is to make a high quality scan and laminate it. I have a credit card sized scan of the ID page.
Of course, this is not complying with the law in some coutries, but like cavorting cheetah, I feel that so long as my passport is within easy reach (usually the hotel reception safe), then most cops will be reasonable about this, as they understand the risks of losing a passport and also that some criminals target these types of document, which is neither in theirs nor your interests.