It’s hard to tell precisely, but I found this page (in French) that gives an history of pronunciation. (Jump to "IV – Principaux phénomènes touchant les consonnes")

Les autres consonnes finales (ex : t) s’assourdissent au VIIIème siècle, et s’effacent progressivement (ça dépend des consonnes), jusqu’au XIIIème. Le r est le plus résistant (XIIIème).

Other (note: other than "m", that disappeared earlier) final consonants (ex: t) grew quieter in the 8th century, and faded progressively (depending on the consonant), until the 13th century. The r was the most resistant (13th century).

In English, it’s very related to the accent, I don’t think it has something to do with French.