The attack revived concerns about anti-Semitism in France, notably linked to the Israel-Hamas war in Gaza, and led to heightened security at Jewish places of worship around the country.
A police officer was injured after the suspect set multiple fires around the Beth Yaacov synagogue on Saturday in the Mediterranean resort town of La Grande Motte.
The suspect, identified by prosecutors only by his initials EHK, fled the scene but was later arrested.
He was injured in the thorax, arm and face during the arrest, France's counterterrorism prosecutor's office said in a statement.
EHK, an Algerian with French residency, was presented to a judge on Wednesday.
Prosecutors said they are seeking preliminary terrorism charges against him including attempted murder and arson committed for reasons of race or religion as well as armed violence against police.
Two other people suspected of providing him help are also facing potential charges.
Under questioning, the suspect admitted staging the attack and told investigators he acted to support the Palestinian cause and make Israeli authorities react, the statement said.
He said he did not have any homicidal intent but wanted to scare people.
Based on questioning by police and his social media posts, EHK appears to have become more radical in his religious beliefs in recent months, and told acquaintances that he wanted to go fight in Gaza, prosecutors said.
He also ''has for a long time nursed a hatred toward Jews, specifically focused on the situation in Palestine,'' the statement added.
In recent weeks he purchased a firearm and conducted internet searches about synagogues in the region, Jewish holidays and Sabbath practices, according to the statement.
He went alone to the Beth Yaacov synagogue on Saturday with a handgun, several plastic bottles full of fuel and an axe upon which he had written statements about Palestine, Gaza and Muslim blood, prosecutors said.
They asked for him to be jailed pending further investigation.
"Once again, French Jews have been targeted and attacked because of their beliefs," caretaker Prime Minister Gabriel Attal said after visiting La Grand Motte.
"We are outraged and repulsed."
