Is tertiary education free of cost in Spain and Portugal? I know that in some EU countries tertiary education is absolutely free (i.e., supported entirely by taxes) if someone knows the languages up to C2 level.
For instance, I know that irrespective of country of origin (EU or Non-EU) tertiary education is 100% free of cost in Germany and Poland if someone is proficient in the native language of those counties up to C2 level.
Is tertiary education free of cost in Portugal and Spain if someone is proficient in the languages of those countries?
No it's not.
You always have tuition fees, which in absolute term may seems negligible (between 1 and 2 thousands euro per year), but it can be a relevant chunk of a family income, considering the average salary being in the 700-900 euro range for most of the people living outside the major, rich, urban zones (Madrid-Valencia-Barcelona-Lisbon-Oporto, to name the largest).
Specifically to Portugal, there is a rule[1] the Ministry of Education establishes a minimum amount that varies each year depending on the minimum national wage rate.
According to Portuguese regulations, the minimum amount of tuition fees students are required to pay is 1.3 times the minimum national wage rate. For the year, 2010, the minimum national wage rate amounted to 475 EUR per month.
For upper education (like Ph.D enrollment) in Portugal the tuition fees may reach easily 2-3000 Euro.
[1] rather absurd, in my opinion Art. 16, comma 2 https://dre.pt/web/guest/legislacao-consolidada/-/lc/107958193/201708090100/73459622/diploma/indice