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There is a technological solution. It's called a coin holder and the Euro version holds the top five denominations in neat spring-loaded cylinders. I had expected to be treated with contempt when mine went into action but most French people regard it with silent - yet undisguised - fascination.
The brown coins I drop into charity boxes which may be what I'm expected to do.
One disadvantage. My holder was bought online from a casino equipment supplier. For some time afterwards I was bombarded with email offers for discounted roulette wheels and poker chips until I de-subscribed.