This author claims that Modern French has words close to Burushaski ones, an assertion I checked with Wiktionary's Burushaski list. French maman is a term of address, not the general term for mother, mère. The Burushaski word for mother is not mama but nani, nana. Etc.
He did find a few coincidences, like French je /Zë/ "I" and Burushaski ja /dZa/, but that's the nominative or subject form in French, and the other forms, oblique and possessive, all have stem m-.
About 50 words as tata, dad, mama, mum, mako, child, viro, man, bena, women, meno, think, gabi, take, da, give, beru, carry, cleu, hear, kahla, speak, edo, eat, itao, go, aro, plough, gabala, head, aedu, fire, bergo, hill, corro, summit, temos, dark, kolo, wheel, bitu, life, maros, big, which can be found in many languages as Gaulish and Dravidian, could come from this original language.
Appendix:Swadesh lists - Wiktionary, the free dictionary
I'll use Proto-Celtic and Proto-Dravidian, with Proto-INdo-European in parens:
father, *phatir (*ph2ter), *appa -- mother, mâtîr (*meh2ter), *amma -- son (child), *makwos, *makantu -- man (male), *wiros (*wiHros), (?) -- woman, *benâ (*gwenâ), *pen -- to think, (variable) -- to take, (variable) -- to give, *dati (*dedeh3ti < *deh3-), *ciy- -- to carry, (?) -- to hear, *klinutor (*klnewti < *klew-), *kuntV -- to speak, (variable) -- to eat, *essi _ *phiteti (*h1ed-) , *uHn _ *tiHn -- to walk (go), (variable) -- plow, *aratrom (*h2erh3trom < *h2erh3-), *namkol -- head, *cwennom, *talay -- fire, *tephnets (*tep- "to be warm, hot"), (?) -- mountain (hill), *moniyo-, (?) -- peak (summit), (?) -- darkness (dark), *temeslos (*temH-), *cînkk- -- wheel, *rotos (*Hreth2- "to run"), (all borrowed from Sanskrit cakra "wheel, disk, circle") -- to live (life), *biwo- (*gweyh3-), *man- -- large (big), *mâros (*meh2- "good"), (?)
For Wiktionary translations, I used Irish and Welsh, and Tamil and Telugu and Kannada and Malayalam.
I found a few matches, but not as many as in that article.