Police in the centre of Paris used tear gas and water cannon to break up a pro-Palestinian rally, after the French government banned such demonstrations.
Interior Minister Gérald Darmanin said those defying it should be arrested as "they are susceptible to disrupt public order.''
Despite the ban, thousands of protesters gathered in Paris, Lille, Bordeaux and other cities on Thursday.
President Emmanuel Macron appealed to people not to foment internal division.
"The shield of unity will protect us from hatred and excesses," he said in a video address.
The ban on pro-Palestinian rallies comes as European governments fear a rise in antisemitism triggered by the Israel-Hamas war.
Hours later, police made 10 arrests and used water cannon to disperse a 3,000-strong rally at Paris's Place de la République, where demonstrators chanted "Israel murderer" and "Palestine will win" and waved Palestinian flags. 10 people were also arrested at another rally in Lille.
Pro-Palestinian groups said the ban risked threatening freedom of expression and pledged to continue demonstrating in support of the Palestinian people.
Charlotte Vautier, who attended the rally, told Reuters: "We live in a country of civil law, a country where we have the right to take a stand and to demonstrate.
"[It is unfair] to forbid for one side and to authorise for the other."
Meanwhile, police in Germany's capital Berlin also banned planned pro-Palestinian demonstrations, citing the risk of antisemitic statements and glorification of violence.
Police said around 60 demonstrators complied with an order to leave Potsdamer Platz on Thursday.
In his video address, President Macron urged the French people to stay united, saying "let's not add national divisions to international divisions".
He described Hamas as "a terrorist organisation that wants the death of the people of Israel".
Some 13 French citizens have been confirmed dead in Hamas' attack on Israel on Saturday.
President Macron said 17 French nationals were missing and were likely among the hostages held by Hamas in Gaza, adding: "France is doing everything it can alongside Israel and our partners to bring them home".
Four children are among the missing.
Israel, he said, had the right to defend itself by eliminating terrorists, but "has to preserve civilian lives because it's the duty of democracies".
"The only response to terrorism is one that is strong but fair," he said.
France has a Jewish community of almost 500,000, the largest in Europe. France's Muslim community is also among Europe's largest - an estimated five million.
Mr Darmanin told regional representatives on Thursday that Jewish schools and synagogues should be protected by a visible police presence.
He told French radio that 100 antisemitic acts had been recorded since Saturday, most involving graffiti showing "swastikas, 'death to Jews,' calls to intifadas against Israel".
Some incidents included people being arrested attempting to carry knives into schools and synagogues, he added.
French police are already guarding the homes of leading MPs. National Assembly President Yaël Braun-Pivet and MP Meyer Habib, who are both Jewish, have been offered further protection.
It has emerged that Ms Braun-Pivet, a member of Mr Macron's Renaissance party, has received death threats.
She had parliament lit this week in the colours of the Israeli flag, and called a minute's silence before an Assembly session on Tuesday.
Ms Braun-Pivet also announced that Maryam Abu Daqqa, a member of the Popular Front for the Liberation of Palestine (PFLP), would be banned from attending a documentary screening in parliament next month. The militant organisation is recognised as a terrorist organisation by the EU.
Meyer Habib represents a constituency for overseas French citizens, which includes Israel and the Palestinian Territories, and is a vocal supporter of Israel. After the Hamas attack he said "we are witnessing the return of pogroms".
French politics has been riven by the Hamas attack and its aftermath.
While most parties have condemned Saturday's "terrorist attack" and expressed support for Israel's right to respond, the initial response from Jean-Luc Mélenchon's far-left La France Insoumise (France Unbowed) party was more equivocal.
A statement by the party referred to the Hamas attack as "an armed offensive of Palestinian forces", prompting fierce criticism from other parties, including left-wing allies such as the Socialist and Communist parties.
Germany's Chancellor Olaf Scholz has declared "zero tolerance" for antisemitism.
He told parliament that pro-Palestinian group Samidoun, which was pictured handing out sweets in the Neukölln area of Berlin to celebrate the Hamas attack, would be banned. "We do not tolerate antisemitism," he added.
Mr Sholz told MPs in the Bundestag that Israel's security was German state policy. German Foreign Minister Annalena Baerbock is due to travel to Israel on Friday in a gesture of solidarity.
According to German authorities, in several towns across the country including Mainz, Braunschweig and Heilbronn, Israeli flags raised in solidarity with the country were torn down and destroyed, sometimes in just a few hours.
