[pm215]

The difference between 'doubt' and 'doute' is the vowel sound, not a presence/absence of 'b'. 'debt' and 'dette' don't sound quite identical to me (as a native English speaker and learner of French) but they're very close and the difference isn't that there's a 'b' sound in there. Maybe it's that French 't' is slightly different.

[housecarpenter]

French t is dental, English t is alveolar---in non-technical language, that means the French t is pronounced slightly further forward in your mouth, compared to the English t.

The English t is also aspirated a lot of the time (though not as consistently at the end of a word as at the beginning), while the French t is never aspirated.

There could be differences between the two short e sounds as well, but that depends more on which particular accents of English/French you're talking about.