Overreaction much? It's a made-up accent in a fictional universe. It can be as caricature-ish as it wants to be.
I mean...have you heard the Antivans? 
Even Fereldan/Free March English accents are sometimes caricatured. Have you heard how Vivienne speaks? It's a caricatured posh English accent if I've ever heard one.
The Orlesians are only depicted as villains because you played Fereldan PCs who have a natural animosity with them. The Orlesians themselves also mock the Fereldan language and customs.
They're still the most powerful nation on Thedas. Are you claiming that the most powerful nation on Thedas is the underdog because Fereldans make fun of the way they talk?
I also disagree with what you said about DAI. The accents are relatively tame compared to those in DA2. I loved Giselle's speech, as well as Celene's. Gaspard's was smexy. 
DAO didn't even have many Orlesians to speak of. There was Riordan who had a "regular' French accent. There was also Isolde who had a "regular" French accent when she wasn't being hysterical (after solving the Connor crisis). Leliana goes without saying.
Only Marjolaine had caricature'd speech.
Agreed in DAO the worse caricatured speech was a villain, Marjolaine. Isolde's accent was pretty heavy, you know, not regular. I would say hers should be the limit before stooping to cartoon levels.
In DAI everybody in Orlais except Leliana and Celene (got to take an empress a little seriously) have a cartoon-level of caricatured accent. So, a decrease in quality and refinement imho.
But I'm not offended or anything. French, like Russians and Italians for mobsters have been used to characterize strange foreigners with strange ways, and often villains, in the English speaking world since forever.
It's not very subtle and appeal to base 'nationalism' and a feeling of superiority - which is kind of well-funded in the modern world, after all here I am - a French person consuming NA entertainment products and talking about them in English on an English speaking forum- towards other cultures imho, but I won't start an Internet protest other that. It only made parts of the game in Orlais less pleasant for me.
One could also ask why have strong foreign accents in a game anyway? The English speaking world is so diverse in its various strong accents (Welsh, Scottish, East Coast American English, West Coast, upper-class Brit English, Cockney, Texas accent, Indian accents) that you can find a way to express exoticism and diversity without resorting to foreign accents.
The likely explanation is that a foreign accent is supposed to be an audio clue to the players that the fictional world is somewhat reminiscent of the country whose accent is used, don't you think?
And Giselle's accent is cringeworthy to my French ears, to be honest. Even Jacques-Yves Cousteau, which is sometimes used in France to characterize a bad French accent in spoken English had a Yale accent compared to that.
I have no doubt that an Italian or Spanish person might say the same about Zevran or Josephine.