Words that are spelled the same in both English and French are true French cognates or vrais amis. Given how many words are the same (in spelling) in French and English, you already have a considerable start to acquiring a large French vocabulary.
Although French cognates may be pronounced differently (almost 100% of the time they are), the spelling is the same. This exact matching between English and French words is one of the great advantages to learning French as an English speaker. In essence, some of the simplest French phrases to learn are ones that have several words the same in French and in English. When you see the following French phrase and pick out the French cognates that you recognize, half of the sentence is crystal clear. For example je vais au cinéma ce week-end regarder un film, the words 'cinema', 'weekend', and 'film' should be recognizable; this makes understanding the whole sentence a lot less work than if there were no French cognates in the sentence.
History of French Cognates
English comes in large part from French roots. If you look in an etymological dictionary, you will find that many English words are derived from French. In many cases, the spelling has changed a small amount (centre-center) and in other cases the spelling has changed so much that you may not recognize the French word as being the root for the English word.
French cognates are words that are spelled the same in English and French. Words that are spelled almost the same, but not exactly, can be referred to as semi-true cognates. One must also be careful with the similarities between English and French because there are several common French phrases that many people 'recognize' as being the same in French and in English, but actually, they mean different things. For example a 'library' in English is not a 'librairie' in French; the latter is a bookstore and not a place to borrow books with your library card. These are called false cognates or faux amis.
Most Common French Cognates
The list of French cognates is incredibly long; the following list is only a small sample of the cognates between English and French. If you thought learning French vocabulary was hard, start with this list, you can learn hundreds of words at once!