As a Parisian speaker of French, I may overhear the problem since I intuitively sort out the quality of sound according to the spelling and the context, but I don’t feel that so many confusions occur at the end of words.
In French, since the final syllable bears the stress, it is least able to lose distinctions. So, the phenomenon jlawler points for Vulgar Latin should not happen in French. Indeed, the /e/-/ε/ distinction is largely lost in the middle syllables of words or phrases, when I feel it is still clearly made at the end. Clearly, some people may make confusions, especially in less frequently used words (e.g. the distinction between lé, fabric or wallpaper strip, and lai, lay [as opposed to clerical], two very infrequent words, is sometimes heard the wrong way round). But I have never been aware of a confusion on poignée/poignet.
The other example you bring in is, not by chance, a future as opposed to a conditional. Well, for the future tense, the link sent by jlawler is very interesting: the French future and conditional are crafted just as explained for Spanish, but, unlike the conditional, the future (at least in France, and for many decades) is being replaced by a new analytic form; in oral (France) French, one wouldn’t say “je ferai” but “je vais faire” in at least 90% of the cases. If you absolutely have to say it, you will pronounce “ferai” just like “ferais”, at least in Paris, hence the current misspelling (always the conditional form misused to note a future). But context normally tells you when it’s a future, and in general it isn’t. Now, since the future tense has dropped out of the oral language, I guess many children first discover it at school, at least for some forms, and at about the same time they learn that the digraph -ai- is pronounced /ε/: this is one of the few consistent rules of French spelling, and the future (and perfect) 1st singular forms are exceptions. (The Wikipedia article says that j'ai, quai, gai should be pronounced with a closed /e/, which sounds awkward to me.) Curiously, the future and still more the perfect are two tenses that are practically out of use.
By the way, I don’t know why we are taught to pronounce a closed /e/ in these forms (chantai, chanterai): I think very possible that at some point it was decided by grammarians in order to help distinguish the forms in oral speech, one or two centuries ago when they still were in use.
But conversely, if you take perfectly usual forms as present perfect of the 1st group and imperfect, j’ai chanté vs je chantais, the distinction always is very clear to the ear. So I don’t think that the distinction is being lost.
We must also note that this /e/-/ε/ opposition has no counterpart, in final open syllables, for the other medium vowel sounds, closed and open o, and /ø/-/œ/: in final positions you can only have the closed /o/ and /ø/ (with the only exception of the donne-le occurrence of final “e muet” in a stressed position, pronounced /œ/, or metalinguistic occurrences when you have to name a word like le, je, ce). So, being asymmetrical, it may be especially weak. The same may occur with the long e/ä opposition in Standard German (/e:/-/ε:/), which has no equivalent for long medium vowels (there are no long open o or ö), and maybe therefore is not consistently maintained.
A last question: has “France a higher population of immigrant second-language learners than Francophone Canada”, as TKR says? I am not sure how much these new dialects take part in this evolution, which I think has begun many decades ago.