The poll, which will worry the president's team, has Socialist candidate François Hollande ahead of his main rivals in almost every category.
The survey, published in Tuesday's Le Parisien newspaper and carried out by BVA, asked about issues including poverty, prices, unemployment, crime and education.
In two areas, far-right Front National leader Marine Le Pen got the best scores. These were crime and immigration.
Even in these two areas, which Sarkozy made key campaign themes in his successful 2007 election, he trailed in third behind Hollande.
In seven other catgegories, which also included the key economic themes of the deficit, economic growth and taxation, Hollande had a strong lead over Sarkozy.
Asked to name the candidate who is most credible on poverty and economic insecurity, 53 percent chose Hollande against 9 percent for Sarkozy.
The president's best score was on economic growth, where he polled 26 percent of the votes, still lagging Hollande on 33 percent.
President Sarkozy also scored better than his rivals on one separate question, which asked who had the stature of a president. On this he scored 46 percent, versus 39 percent for Hollande, 37 percent for the centrist François Bayrou and just 13 percent for Marine Le Pen.
While Marine Le Pen performed well on her key issues of immigration and crime, voters' uncertainty about her economic plans were revealed by just six percent feeling she was credible on growth and only eight percent on the public debt.