It pays to increase your word power!
First, the good news. Because French has had such a profound influence on the English language, these two tongues are full of cognates--words that are extremely similar because, in essence, they are the same word. Examples include chat for cat, papier for paper, information for information, nuit for night, and so on. The presence of so many cognates makes the assimilation of French vocabulary much easier. Moreover, the comparative ease of reading French (because it is written in a Latin alphabet) means that new words can be assimilated easily in reading practice.
Now the bad news. First, the vast majority of French words are not cognates. Second, French nouns take gender. That is, almost all French nouns are either feminine or masculine. This has implications for which articles they take (le vs la, un vs une), and also for other words that modify them, particularly adjectives and adverbs. Accordingly, when studying French vocabulary, it is best to memorize not only the word itself, but also its gender. Don't learn the word as livre (book), but as le livre (the book--a masculine noun). It's worth the extra effort, and will save you much grief in the future.
Here are some resources for French vocabulary.
Common French Nouns - Flashcards from Quia. 200 words to get you started.
Exercises Vocabulaires - Vocabulary exercises, by word category. Nice resource.
Francais Interactif - Hey, forget this site. Francais Interactif is absolutely the best French learning resource on the the net, and it's free. Each chapter comes with vocab. If only they'd had this when I was taking French at University. Please do check it out.