PARIS—Europe’s most prominent artificial-intelligence developer is tapping the continent’s biggest tech giant for cash to keep up in the global AI race.

Dutch chip-equipment giant ASML is pumping more than $1.5 billion into France’s Mistral AI for an 11% stake, leading a round valuing the Paris-based startup at nearly $14 billion—more than double its valuation last year. The ASML funds come as part of a roughly $2 billion round that Mistral says also includes Yuri Milner’s DST Global and French state-owned investment bank Bpifrance.