This is a specialisation of the How to handle moving between countries with different tax year dates question, for what seems like one of the specific edge cases from it.
France uses calendar years for tax years, while the UK for complicated historical reasons uses 6th April - 5th April for personal tax years. As I understand it, from the UK-France tax treaty, if you spend more than half of a year living and working in one of the two countries, then you'll count as a tax resident in that country but not the other.
What happens if you move from France to England in September though? For the sake of argument, let's say you move + change jobs on Saturday 6th September 2014. By this point, you'll have spent more than half of the French tax year (2014) in France. However, you'll also then spend more than half of the UK tax year (2014-2015) in the UK.
In such a case, what things do you need to pay tax on in France, what things do you need to pay tax on in the UK, and what things at the higher rate of the two? Secondly, what French tax-resident savings can you take advantage of / not, and what UK tax-resident savings can you / can't you take advantage of?