The Norman inheritance
After 1066 the ruling class spoke French for three centuries. Law, government, food and warfare vocabulary in English is largely French: justice, parliament, beef, army.
Cognates you can trust
Words ending -tion, -ible, -ment and -aire are usually near-identical in both languages: information, possible, gouvernement, dictionnaire.
The traps
Faux amis look familiar and mislead. 'Librairie' is a bookshop, 'actuellement' means currently, and 'sensible' means sensitive.