Hollande's visit comes almost two decades after French nuclear tests in the South Pacific drew fierce criticism of Paris from Australia.
Hollande is leading a major business delegation and seeking to "strengthen the historic links and economic relations" between the two countries, his Elysee office said in a statement.
"We are in a position where we can have closer and further economic ties," Hollande told the Australian Business Council.
"What I am saying is we need to push our aspirations further," he added, describing French companies such as satellite giant Arianespace as at the "forefront of technology".
He was officially welcomed by an honour guard and a 21-gun salute in parklands on Sydney Harbour.
Paris-Canberra ties suffered during nuclear testing in Polynesia in the 1990s and the sinking by French agents of the Greenpeace ship Rainbow Warrior in Auckland in 1985 as it prepared to lead protests around Mururoa atoll.
However Australia and France signed a strategic partnership in January 2012 and have worked closely on Afghanistan, Syria, Iran and other major crises in recent years.
French officials said they see strong opportunities to develop trade with Australia.
"We have a card to play in this country which is in its 24th year of uninterrupted growth and has launched major projects in sectors such as telecommunications, new technologies, infrastructure and transport," said one official.
Hollande's delegation includes heads of France's leading companies such as Arianespace, the national rail firm SNCF, the Vinci construction company, energy giants GDF Suez and global luxury house LVMH.
Trade in goods and services between the countries was worth US$6.9 billion (€5.4 billion) in 2012-2013.
The French leader, who arrived from New Caledonia after attending the G20 in Brisbane at the weekend, was to visit the capital Canberra on Tuesday.
In Noumea, Hollande vowed Paris would remain neutral in a self-determination referendum that is due to be held in the French Pacific territory by 2018.
"It's the Caledonians who will have the last word," Hollande told members of the local Congress on Monday.
He was due to meet Prime Minister Tony Abbott on Wednesday when he would also lay a wreath at Australia's War Memorial.
Some 400,000 Australians -- 10 percent of the population -- fought in World War I and of the 60,000 who died, 40,000 of them fell in France.
Hollande will throw a reception Tuesday evening at Sydney's iconic harbour-front Opera House for the French community which has been boosted this year by 26,000 youngsters on working holiday visas.