What is the correct word for a speech which is not smooth and with lot of stops ( probably the speaker is not able to find the right english words )
"Disfluency" is probably the word you're looking for, it's the technical term describing almost exactly what you're saying:
EDIT - it depends on whether you want to refer to the lack of smoothness itself, or to the speech. "Halting" or "hesitant" might be better adjectives in the latter case.
speak haltingly - is probably what you want, but it does not necessarily carry the connotation of language fluency, as it could pertain to someone who was scared to talk.
stuttering speech - might be reasonable, depending on the context, but only if the person knows the words, but can't find them and is physically attempting to articulate the word by initiating the first syllables.