That's with every dialect of English. English has phonemic stress, i.e. the way you stress a word can change its meaning or make it unrecognisable unless you're speaking to an English-speaker familiar with people who speak English coloured by whatever your native language is. This is a particular problem for French-speakers, since French doesn't have phonemic stress.

British and Irish people will probably understand French-accented English better than Americans because of greater exposure to French.

True, but aren't you primarily talking here about vowel length? As a language feature it's more pronounced than accent/stress.

/ˈmaʊntɪn/ MOUNtain

/mɒn'taɪn/ mounTAIN (?)

https://en.wikipedia.org/wiki/Vowel_length

Reminds me of foreigners asking for "water" in the US at restaurants, having to pronouce it "wadder" in order to be understood.

I remember a grad student who went through a similar incident. While I appreciated his frustration, I also understand the anxiety of the poor server trying to remember how to mix a Woahtuh before my colleague decided to enunciate the coda.