Hollande was speaking in front of the Shoah Memorial in Paris, just over two weeks after 4 people were killed in an attack on a Jewish supermarket a few kilometres away.
Meanwhile new figures released on Tuesday show the number of anti-Semitic acts doubled in France in 2014, according to the CRIF, the umbrella organisation which officially represents French Jews.
The organisation said some 851 anti-Semitic acts were registered in 2014, compared with 423 the previous year, with acts of physical violence jumping from 105 to 241.
“These anti-Semitic acts represent 51 per cent of racist acts committed in France, while Jews make up only one per cent of the population,” said the CRIF in a statement.
France is home to Europe’s largest Jewish population, estimated to be between 500,000 and 600,000, as well as the continent’s largest Muslim population, estimated at around 5 million.
In demonstrations over the conflict in Gaza last summer, violent anti-Jewish obscenities were heard on the streets of Paris and some Jewish businesses were destroyed in Sarcelles, just outside the capital, where there is a sizeable Jewish community.
Recent figures show a record number of Jewish people are choosing to leave France and settle in Israel or elsewhere, citing anti-Semitism and the economic downturn as reasons for their departure.
Before making his speech, the French president joined a group of youngsters listening to holocaust survivors tell their stories.
The French president then announced that by the end of February the government will present a new plan to tackle racism and anti-Semitism.
The plan will include security provisions, a new emphasis on teaching about the holocaust, and measures to stop the propagation of hate speech and racist or anti-Semitic ideologies on internet.
This afternoon Hollande is to join other world leaders at a gathering in Auschwitz where 1.1 million mainly European Jews, 76,000 of them French, perished.
In all, the Nazis killed 6 million of pre-war Europe’s 11 million Jews, as well as large numbers of homosexuals, gypsies and political opponents.