Similar in some vocabulary. Different in general structure and grammar. Indeed they do both use the modified Roman alphabet (not the Arabic alphabet!), as doe most European languages.
English is basically a Germanic language which has borrowed many words from languages from many parts of the world, including French words.
French is one of the group of "Romance" languages, i.e. languages which come from Latin, as spoken in Rome.
Depends what you call similar. They're both Indo-European, so they're more similar to each other than they are to, say, Navajo or Zulu. But they belong to different branches of the Indo-European language family; French is a Romance language and English is basically Germanic with a considerable Scandinavian and Romance influence.
"Similar" isn't a technical linguistic term. English is a Germanic language that was spoken in a country that was suddenly invaded and taken over by a bunch of Frogs in 1066, after which a shitload of Frog vocabulary was added. The grammar has a bunch of differences with both German AND French.
The French and English languages are related in a sense, because French is a Romance language descended from Latin with German and English influences, while English is a Germanic language with Latin and French influences. Thus, they share some similarities, most notably the same alphabet and a number of true cognates.
French and English have hundreds of cognates (words that look and/or are pronounced alike in the two languages), including true cognates with similar meanings, false cognates with different meanings, and semi-false cognates—some similar and some with different meanings.