I know that Irish and Scots Gaelic carries with it the similar notable 'ch' sound heard in German and Dutch, yet I wonder because of historical names which languages and culture the Celts were closer to. For example the people of what has become mostly France were called and considered the Gallic people, and naturally these names sound similar to the British Isles "Gael." Naturally a lot history of peoples can be derived from linguistic evolution (such as we see with Sanskrit's ancient connections to many Indo European languages). Furthermore and besides linguistics, what does DNA relativity and closeness of modern European peoples tell us?
Whether or not the Celtic and Italic languages should be grouped together and assumed to have a more recent common ancestor than they do with other Indo-European branches really depends on which historical linguist you ask.
They do have significant common features and are often grouped together, but whether these similarities are due to genetic relatedness or to the geographical proximity (remember Celtic languages were once spoken as far east as Turkey and they had a large overlap with areas where Italic languages were spoken) is a matter of debate.
There isn't a wholesale rejection of the common ancestor hypothesis, but it isn't sufficiently supported by the evidence to be preferred by most experts over the alternative - that these language families existed together with substantial borrowing taking place.
I suggest /r/linguistics if you want a more detailed answer.