Can I set Eclipse to ignore "Unhandled exception type"

Is it possible to get Eclipse to ignore the error "Unhandled exception type FileNotFoundException".

No. That would be invalid Java, and Eclipse doesn't let you change the rules of the language. (You can sometimes try to run code which doesn't compile, but it's not going to do what you want. You'll find that UnresolvedCompilationError is thrown when execution reaches the invalid code.)

Also note that just because the file existed when you called file.exists() doesn't mean that it still exists when you try to open it a tiny bit later. It could have been deleted in the meantime.

What you could do is write your own method to open a file and throw an unchecked exception if the file doesn't exist (because you're so confident that it does):

public static FileInputStream openUnchecked(File file) {
    try {
        return new FileInputStream(file);
    } catch (FileNotFoundException e) {
        // Just wrap the exception in an unchecked one.
        throw new RuntimeException(e);
    }
}

Note that "unchecked" here doesn't mean "there's no checking" - it just means that the only exceptions thrown will be unchecked exceptions. If you'd find a different name more useful, then go for it :)