François Hollande, France's first Socialist leader in nearly 20 years, promised to restore dignity and simplicity to the French presidency as he took power in a deliberately low-key ceremony on Tuesday then immediately flew off to meet the German chancellor on a quest to temper Europe's austerity drive.

Hollande, who has styled himself as Mr Normal, used his Elysée palace inauguration to set himself apart from the politics and celebrity style of his rightwing predecessor, Nicolas Sarkozy.

In his first speech he promised "a new path" for Europe, insisting growth measures to kick-start economies would go hand in hand with the reduction of public debt. He vowed his five-year term would be fair and just. He said he would unite France and bring the divided country much needed calm and reconciliation.

In a series of digs at Sarkozy, who had been dubbed the president of bling bling, Hollande, in his speech in Paris, promised "scrupulous sobriety of behaviour". He saluted the contributions of previous French presidents, including Jacques Chirac's attachment to the "values of the republic", but stopped at citing any Sarkozy achievements, saying simply he wished him well in his new life.

Hollande acknowledged the hurdles he faced: "A massive debt, weak growth, high unemployment, degraded competitiveness and a Europe that is struggling to come out of crisis."

As if the crisis-hit eurozone needed another metaphor for doom, the new president's first day in office was accompanied by thunder and lightning storms of epic proportions.

First he was soaked by a torrential downpour during his victory tour along the Champs-Elysées as he stood up, exposed to the elements in an open-top car, waving at the crowds and blinking through the downpour. He left the car to light the traditional flame to the unknown soldier at the Arc de Triomphe so soaked to the skin that his shirt was transparent and droplets rolled down his forehead. Then the French presidential Falcon jet was hit by lightning minutes after taking off from Paris for his working dinner in Berlin and he was forced to turn back.

Hollande boarded a second plane and went on to meet Angela Merkel while political commentators back home cracked jokes about Zeus and the rain gods.

Sarkozy, meanwhile, encountered only sunny spells, first during his final departure from the Élysée, waving from his car window, then as he emerged hours later in his running gear in front of TV cameras for a post-presidential jog around a Paris park under a rare moment of blue sky.

When a reporter in the Élysée courtyard called out to a soaked Hollande, "you are not afraid of the rain?", he smiled and shot back, "I am not afraid of anything".

Hollande, who calls himself an ordinary guy, had been keen to keep the pomp-filled presidential inauguration as modest as possible and set himself apart from the unpopular glitz of Sarkozy. As he was driven to the Elysée from his apartment in a hybrid Citroën, television commentators marvelled that his car did stop at red traffic lights and went no faster than 50km an hour. Stepping on to the red carpet rolled out over the Élysée courtyard gravel, his tie was noticeably wonky.

Hollande's guest list was distinct from that of five years ago for Sarkozy, who put his wife, stepdaughters and sons centre-stage, opening up a new chapter in the blurring of boundaries between public and private life in France. Hollande had about 30 private guests joining the 350 officials at the event. His partner, the political journalist Valérie Trierweiler, was present, but their children were not, and journalists judged her outfit "very elegant" while taking care to add it had been "chosen from her wardrobe" that morning.

His guests included the writer Mazarine Pingeot, daughter of the Socialist president François Mitterrand, and the entrepreneur Pierre Bergé, the entrepreneur, partner of the late fashion designer Yves Saint Laurent and co-owner of Le Monde.

Before taking office, Hollande spent more than 30 minutes in a private meeting with Sarkozy, during which he was handed the codes to France's nuclear strike force. After a handshake Sarkozy, staying true to his glamorous approach to taking office alongside his second wife, Cécilia, left the palace walking down the red carpet hand in hand with his third wife, Carla Bruni-Sarkozy. As his car drove away, supporters, reportedly organised by his right-wing UMP party, cheered and said "thank you Nicolas". Earlier they had booed key Socialists arriving for the inauguration.

Hours after taking office Hollande put his own twist on proceedings by laying a wreath to Jules Ferry, pioneer of France's free and secular state education system. In front of schoolchildren and dignitaries he stressed that education was at the heart of his mission, that he would stay true to his promise to create 60,000 more posts in schools in the next five years – a move the right had denounced as spending madness. But he distanced himself from what he called the "moral fault" of Ferry's backing of colonial expansion.

A second symbolic gesture was the laying of a wreath in memory of Marie Curie, the Polish-born, Nobel-prize winning, scientist. It was a message not just about France's need to invest in research but also about accepting foreigners.

The only reminder of the quasi-monarchical pomp of the French presidency was Hollande's third speech, of the day, in the luxurious salle des fêtes of Paris's city hall, with its throne-like chairs and gold chandeliers recalling Versailles. Hollande vowed to project the "best image" of France, saying his overriding aim and motto was justice.