This epoch in European history was Celtic. But now only a small peninsula on the continent is inhabited by descendants of those powerful people. Bretons in France can be proud - they were the only who survived in continental Europe. Celts are also represented by Irish Gaelic, the Scottish Gaelic and Manx Gaelic; Welsh and Cornish languages in Ireland and Great Britain.
The continental subgroup of Celtic languages is now extinct, Gaulish, Lepontic and Celtiberian languages died out, that is why we can judge about Common Celtic only by the remains of Continental subgroup and by living Insular subgroup languages. What we know about the Common Celtic phonetics, is that: the vowels remained long and short, the syllable vowels turned into CV or VC forms (C - consonant, V - vowel), diphthongs tend to be dropped, consonants lost aspirants, but somewhere preserved palatals. Final consonants (important in endings) were often dropped, as well as the initial ones.
Common Celtic shows no initial mutations, lenition or nasalisation etc. Gaulish did not have them either. This is the feature that was developed in Insular Celtic epoch, though arguments are still under way.
Irish morphology was similar to its predecessor Proto-Indo-European. It had, supposedly, 3 genders, though neuter became extinct very early; three numbers and 5 or 6 noun cases (nom., gen., dat., acc., voc.). Some noun endings show archaic instrumental case in dative constructions. The common Celto-Italo-Venetic -b-, -bh- is used in dative plural and dual. The adjective was declined like a noun and had 4 degrees of comparison (plus equalitive, comparative, superlative). Pronouns that can be reconstructed are quite scarce including the only demonstrative sindos (this) which finally became an Irish definite article an or Manx yn.
And practically nothing is known for sure about the verbs in Common Celtic. They must have had forms and inflections that had not gone far from Proto-Indo-European ones.