This is not an objective question considering there is no cut and clear definition of indigenous people of Europe.
If you mean who were there before the Indo-European language speakers, then the answer would be ‘[Western European Hunter Gatherers](https://en.wikipedia.org/wiki/Western_Hunter-Gatherer)’ and ‘[Eastern European Hunter Gatherers](https://en.wikipedia.org/wiki/Eastern_Hunter-Gatherer)’.
The contemporary nations that you can trace back to have been the oldest peoples to survive the Indo-European migrations would be the Basque people and The Finno-Ugric people.
TLDR: **Basque people** (Minority in France and Spain)
**Finnish people** (Finland)
**Sami people** (Sweden/Norway/Finland)
**Estonian people** (Estonia)
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