Now that was something I did not know about Russian, but thinking about it, there's been a few times when I've seen people speaking English with Russian accents on TV and movies where they have spoken like that, "I put cup on table".A lot of what identifies a speaker as being a non-native English speaker is not necessarily an 'accent' (the way they say particular words) but the patterns of speech. (Which would include all those unconscious noises we make as we talk.)
A drama teacher of mine pointed out that the Russian language doesn't have articles. They have no words for 'The' or 'A' in Russian. So where a native English speaker would say, "I put a cup on the table." A Russian would say (the equivalent of), "I put cup on table." - which, confusingly, could mean:
"I put the cup on a table"
"I put a cup on the table" - you would have to have context to know which.
And similarly a British 'don't interrupt me, I'm uncertain but thinking" noise might be "erm..." a Russian would be more likely to make a much more nasal, "Gnnnea..." sound. I'm not sure writing "Gnnnea..." on the page would make the reader think the character was more Russian but an actor would use that. But if I was writing a Russian character I would lose as many articles from his speech as possible. Especially at times of stress. People revert to their normal speaking voice /patterns when pressured.
There is no 'continuous present' tense in French. "Je fais" means 'I do [something]' and ‘I am doing [something]’.
German tends to have the verbs at the ends of the sentence: (to use Danny's cliché example) "For you the war is over."
Non-native speakers will often say things in English that sound slightly 'off' somehow to us but make perfectly grammatical sense to them.