Only two things in the world are more difficult than French pronunciation: French grammar and, of course, English pronunciation.
First I'll give you a few hints to hide your Texan
origin. Then you'll find, for your convenience, an alphabetical list
of letters and how to pronounce them in French.
Please, do not pronounce "é" as "ay"
A very easy way, for a Frenchman, to make fun of Britons or
Americans is to add the sound "y" everywhere. It's such a common
mistake that I suppose teachers spread it on both sides of the
Atlantic Ocean.
"é" is what the International Phonetic Alphabet writes
e, i.e almost like the "e" in "very" but with the mouth less open.
This mistake illustrates a fundamental principle, which in my
opinion should help you to understand how French pronunciation works:
French vowels are simple, while English vowels are composite.
In particular, the French language has no diphthongs. Simple
here doesn't mean easy. It means that only one flat sound, one
phoneme, is involved in the utterance of a vowel. Therefore, "é"
does not end with some glide to "y". It may last as long as you want,
but the sound at the end of the vowel is the same as it was at the
beginning.
In English, on the contrary, one written vowel often corresponds to two phonemes. The obvious case is the diphthongs: "sound" (a->u), "twice"
(a->y). This is also true of many other vowels, which sound gradually glides to another sound (typically "y"). See other examples in IPA/ASCII Representation of Sounds in English. Thanks Mercuryblues for his indications about this issue.
In the same way, a French sentence is very flat. In English, you
need to put a stress on some syllable and half-pronounce others. In
French, you pronounce most syllables (apart from the case of the mute
e, see below); they all have approximately the same weight. In normal
speech, you should stress only the last syllable in a group of
words, even in a very long word like anticonstitutionnelle'ment. Example:
'French 'vow[e]ls are 'simpl[e], while
'English 'vow[e]ls are 'comp[o]sit[e]
Les
voyell[e]s fran'çais[e]s sont simpl[e]s,
tandis que les voyell[e]s an'glais[e]s sont
compo'sées.
However, ancient French did contain diphthongs. That's the reason
why the written language contains so many digrams, ie. groups of
vowels which correspond to only one phoneme.
Miscellaneous
Double consonants are almost always pronounced like one
consonant. "belle" and "bêle" sound exactly the same.
A consonant other than c, r, f, l
(tip: careful) at the end of a word is usually mute. We will
see exceptions below. Example:
clef: klé (key, also spelled
"clé")>
Non-French words. Some languages modify the spelling of
foreign words to match the foreign pronunciation (fútbol in
Spanish). Others keep the foreign orthograph but pronounce it as if
it was a local word (English). Modern French usually keeps both the
foreign orthograph and, as much as possible, the pronunciation. More
and more French people pronounce the jota in Spanish names although
this sound normally doesn't exist in French.
However, the French knowledge of foreign languages has well-known
limits. Furthermore, stressing will always be done the French way, i.e
on the last syllable. So "week-end" (weekend) will be pronounced "wik'ènd"
(while a pure French pronunciation may be "wékan" or
"vékan", and a pure English pronunciation would be something like
"'wiikend").
Written accents. We will see below the accents that indicate
the pronunciation (é, è, ê). Other accents
(à, ô, û, etc) only serve to avoid ambiguities in
written language (a vs à, eu vs eû...). Or they indicate the
etymology of the word. In either case they have no effect on
pronunciation.
Alphabetical list
Now, we may examine in detail how to pronounce written French
words. Here is an alphabetical list of letters or group of letters
that sound differently in French and in English.
Of course, since we are speaking about the French language, there
are many other exceptions, for example in popular pronunciations: je
ne sais pas: chépa (I don'k know, or I dunno) ouais for oui (yes)
Another approach of French pronunciation (more academic and a
little less real in the way it differentiates open and closed vowels):
http://www.frenchlesson.org/grammar/pronun/. I have used some of their
examples.
Many thanks Mercuryblues, sloebertje and tdent for corrections!