I agree with Lou, that the calls match Short-toed treecreeper.
Please note, that Short-toed treecreeper can call extremly like an Eurasian TC on rarer occasions, that is hardly distinguashable to the human ear (sound recordings and analizes might be a different story?).
More, you filmed two birds that seems to interact in some way. Its either a pair during display or some kind of territorial defense (both look similar to me, as I dont have enough experience). But I have heard ST-Treecreeper making higher pitched, shrill, Blue Tit like calls on such occasions.
Said that, I must admit, that I have looked for stills in your video, where ID can be supported by plumage. Because your bird seems to show pure, bright white underparts, even on the rear flanks. I know, Short-toed treecreeper are said to get greyer and whiter towards the east, but such, bright pure white flanks (as they appear in your video) are extremly rare in Short-toed treecreeper in central and western Europe (I dont speak of birds with all-whitish underparts and flanks), but long bill is also better for a Short-toed treecreeper.