WHEN in trouble, ditch the prime minister. This has been a guiding principle of many modern French presidents, who enjoy sweeping powers to change prime minister as they please. François Mitterrand, a Socialist president, went through seven; Jacques Chirac, his Gaullist successor, used up four. With his popularity crumbling like a buttery croissant and local elections approaching, François Hollande needs a fresh start. But the calculation over a reshuffle is far from simple.When voters go to the polls for local councils in late March and for the European Parliament in May, Mr Hollande will face his first nationwide electoral test since winning the presidency in May 2012. Although his Socialist Party will probably retain the Paris mayoralty, the overall result is likely to be crushing. Voters are fed up with Mr Hollande. His poll rating fell in March to 17%, according to TNS Sofres, a pollster, lower than any other modern president at this point in his term. In another poll, which a French newspaper decided not to publish, 56% thought that Dominique Strauss-Kahn, the disgraced former IMF boss, would do a better job.Mr Hollande’s private life has made him faintly…