"The international community must be very firm in its handling of this latest provocation," Macron said in a statement, calling on the UN Security Council to "quickly react" to the escalation.
Pyongyang declared Saturday night's test, its biggest ever, a "perfect success".
It triggered an 6.3-magnitude tremor near the test site, according to South Korean experts, and the shock was felt in the Chinese border city of Yanji and the Russian Pacific port of Vladivostok.
Macron called for international pressure to force North Korea to "reengage in dialogue" and "proceed to the complete, verifiable and irreversible dismantling of its nuclear and ballistic programmes".
After speaking to each other on the telephone, he and German Chancellor Angela Merkel called for sanctions against Kim Jong-un's regime to be toughened, a German statement said on Sunday afternoon.
China joins condemnation
Hydrogen bombs, also known as thermonuclear devices, are far more powerful than the relatively simple atomic weapons the North is believed to have tested so far and could be attached to its ballistic missiles.
Pyongyang ally China issued a "strong condemnation" of the test.
So did the UN's International Atomic Energy Agency and the leaders of Japan, South Korea and Russia.
US President Donald Trump said that "appeasement with North Korea will not work" and said the country was a "threat and an embarrassment to China".