Please let me quote what Laura says in about.com (this page: http://french.about.com/od/mistakes/a/beginning.htm)
"French accents indicate the correct pronunciation of a word, and are required, not optional. Therefore, you need to make an effort to learn what they mean, which words they are found in, and how to type them. "
Think of and add the accented characters, with their phonic mapping as separate additional alphabet entries with unique names in the alphabet: basic, acute, grave, caret, circumflex, cédille, cedilla ...
If they are not uniquely named and exploited from your alphabet then when to use them will be clear as mud to you