Some 49 percent of voters expressed confidence that Hollande is able "to deal effectively with the major problems facing the country", according to the CSA poll published in the Le Figaro daily.
The president polled 54 percent in July and 50 percent in June.
Support for the prime minister Jean-Marc Ayrault also fell, by four percent to join Hollande on 49 percent.
Some 47 percent of voters do not trust the president and four percent were undecided. For Ayrault, the equivalent figures are 42 percent and nine percent.
The weakening support is not unprecedented however, with the pair's predecessors – Nicolas Sarkozy and François Fillon – also experiencing a decline in support in August 2007.
Sarkozy was however able to keep more than 50 percent of the French electorate on side until January 2008, the newspaper observed.
The twin problems of high unemployment and the economic crisis are of particular concern to French voters, with 62 percent of respondents stating the belief that the government is not sufficiently active.
In a survey of the political popularity stakes, François Fillon retained his lead with 55 percent of voters expressing positive sentiments, followed by Alain Juppé on 53 percent and Manuel Valls on 49 percent.
The poll was conducted by telephone on August 21-22 and involved 998 people.