French economic growth firmed at the start of the year, while Spain’s recovery continued at a steady and strong pace, according to figures released Friday.

French gross domestic product expanded 0.5% in the first quarter from the final quarter of 2015, when it grew 0.3%, national statistics agency Insee said. Economists polled by The Wall Street Journal had expected 0.4% growth at the start of the year.

“Solid growth is getting under way,” French finance minister Michel Sapin said.

A preliminary estimate of eurozone GDP will be published later Friday.

In France, consumer spending rebounded sharply after a lull at the end of 2015 and business investment growth accelerated. The strength of those domestic growth engines more than offset a 0.2 percentage point drag on GDP from foreign trade.

The figures mark the third straight quarter of GDP expansion and support President François Hollande’s claim that the economic situation is improving after years of near stagnation.

But the steady pace of the recovery has so far proved insufficient to halt the rise in France’s public debt or make a significant dent in near record-high unemployment.

The government’s latest attempts to boost job creation by loosening labor laws have sparked widespread protests, some of which turned violent Thursday. Business leaders now fear Mr. Hollande, whose popularity has sunk back to record lows, will back away from any significant overhauls to boost the economy this year.

Gilles Penet, who runs OPS, a Burgundy-based furniture maker, said small companies like his don’t have enough certainty to make large investments. Prices for his goods are weak and demand from his customers—mainly large French retailers—continues to fluctuate.

“The recovery in consumption isn’t as strong as people want to make us believe,” Mr. Penet said.

The uncertainty comes despite a number of strong tailwinds for France and the wider eurozone.

Along with low oil prices that are putting cash in the pockets of consumers and businesses, the European Central Bank’s quantitative easing program to spur inflation out of a prolonged lull has flooded the economy with cheap loans. The monetary easing boosted growth by 0.3 percentage points in France last year, according to estimates from the Bank of France.

The ECB said it could do more to boost inflation if necessary, but insists the ball is now in the court of governments to undertake economic overhauls to fuel growth.

In France, the pace of overhauls has slowed. Faced with street protests in March, Mr. Hollande backed off from changes to labor laws that would have clarified conditions for laying off workers, capped court-ordered severance awards and given businesses greater latitude to negotiate with their employees. His government has presented a modified labor bill that infuriated business leaders who say the changed plans will do more to discourage than encourage job creation.

“This labor bill has become a political tool rather than an economic tool for jobs,” Pierre Gattaz, the head of France’s largest business lobby Medef, said earlier in April.

Finance minister Mr. Sapin said the first quarter figures show the economy is safely on path to reach the 1.5% growth target he has set for 2016, even if quarter-on-quarter figures slow slightly.

“Our action is bearing fruit. We will continue with determination in coming months,” he said.

In Spain, the economy grew at an unchanged rate of 0.8% during the first quarter. That was despite a period of political uncertainty economists feared would hinder consumer spending and investment.

Spaniards are set to vote a second time in June after no single party won an outright majority in December elections. Most polls suggest that the outcome of a new round of voting wouldn’t be much different than the last one, leaving many voters unclear about how parties will cobble together a government—and what their tax and other economic policies might be.

The chief executive of Banco Santander SA, the largest bank in Spain and the eurozone by market value, was sanguine on Thursday at an earnings presentation.

“The recovery is sustained,” José Antonio Álvarez said. Political uncertainty could chip away at economic growth by a tenth of a percentage point, Mr. Álvarez added, but it won’t derail Spain’s strong growth.

And while Spanish consumer confidence levels have fallen since the beginning of the year, they are still close to precrisis levels, when consumption grew strongly, notes Ignacio de la Torre, chief economist at boutique investment bank Arcano Group in Madrid. Car sales are also up.

“During 2016 and 2017, Spain will enjoy greater economic growth than many of its neighboring countries as wages recover,” Mr. de la Torre wrote in an April research report. Spain “will continue to generate large volumes of employment and real estate continues with its recovery.”