Who could really confirm that all these words contained in this list are really from Gaulish origin ?; alouette could have derived from the same root as the estonian (finno ugric) word lὂoke, like ardoise and the turkish arduvaz, berceau from the root that produced the hungarian word bölcso, etc. In many (if not all) examples the synonymous words are quite different in Irish gaelic and in Welsh. In other words, all the terms considered from Gaulish origin could come from non-IE as it could not be connected to any Celtic or Latin words and other IE families languages. 

The continental celtic terms are probably very similar to the Latin and Italic ones. The function words are mostly more reliable to determine what is from Gaulish origin or not, see 'Discussion' in Gaulish (language); the similarities with contemporary French words are in some cases astonishing and closer to Latin or what were Italic languages. In my opinion, there is not doubt that Italic and Celtic languages (especially Continental celtic) were once in the same group that formed the Italo-celtic family languages as the Balto-slavic group and probably the Germanic languages are from the same branch.