PARIS — President Francois Hollande has suffered a dramatic decline in popularity during his first six months as leader of France, failing to convince much of the country that his Socialist government is capable of firm leadership to overcome a persistent economic slump.

Recent opinion polls have shown Hollande sinking nearly 20 points in approval ratings, to about 40 percent, with respondents from across the political spectrum expressing disappointment as unemployment rises, factories close, and growth remains elusive.