There's toponomastic evidence of IE substrate languages spoken in parts of Europe before the historical attested languages. One of them is the Old European hydronymy language (Krahe's Alteuropäische). OEH looks like an archaic IE language (even more than Anatolian), with predominance of the vowel /a/ and lack of inflection. In this way, it would reflect the stage called IE I or "pre-flexional" by Rodríguez Adrados1.
I adscribe to this substrate Celtic *nantu-/*nanto- 'stream, valley', from PIE *dhen- 'to run, flow' (cfr. Latin fōns, fōntis 'spring, source'), with assimilation of the initial dental to the following nasal in the source language (that is, PIE *dh- > *d- > *n-).
Another IE substrate found in SW Europe is Italoid (aka Sorotaptic), which according to linguists Joan Coromines and Francisco Villar was somewhere between Baltic and Italic in the IE dialectal cloud.
In his last book, Prof. Koch of the University of Wales postulates Tartessian (found in inscriptions of SW Iberia dating back to the 7th century BC) as a Celtic language with "aberrant" features like uar- < *ufor- 'over, on', with /a/ instead of the expected /o/ (cfr. Old Irish for). This apparent contradiction could be explained if Tartessian had an Italoid substrate.
According to Villar, IE had a 4 vowel system /i, E, A, U/ until the reduction of *H2e > a introduced a new central vowel in the system. In some languages (Celtic, Italic, and Greek), /a/ pushed /A/ back into /o/, while in Italoid (and also Germanic, Balto-Slavic, Indo-Iranian) they merged into a single vowel.
There's an Italoid lead inscription (now lost) found in Amélie-les-Bains/Els Banys d'Arles (Roussillon) which has been studied by Coromines2. It's a votive text dedicated to the nymph deities called KANTAS NISCAS. The first word derivates from PIE *kwento- 'holy' and the second one is the Iberian counterpart of Basque neska 'girl' < *neś-ka3 < PNC *nusA (˜ -o-) 'daughter-in-law'.
Latin has loanwords from Italoid like vagus 'wanderer' < IE *weg´h- 'to carry (in a vehicle)'.
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1 See for example his Nuevos estudios de lingüística indoeuropea (1988).
2 Els ploms sorotàptics d'Arles, in Entre dos llenguatges, vol. II, p. 143-146 (1976).
3 Iberian niś is found as an anthroponym formant in inscriptions and -ka is a diminutive suffix.