The companies announced that they will enter the competition for the West Coast Partnership franchise, which will include services on the existing West Coast route from 2019 and initial HS2 trains between London and Birmingham from 2026.
See also: Hedgehogs stand in the way of HS2 plans
If the bid is successful it would increase the proportion of Britain's rail network run by overseas operators.
Half of the partnership would be owned by Stagecoach, with SNCF taking a shareholding of 30% and Virgin 20%.
Virgin Trains co-chairman Patrick McCall said: "I'm delighted that SNCF has come on board, and together we will put forward what we hope is the winning bid for the next West Coast - and first HS2 - franchise.
"We've just celebrated 20 years of Virgin Trains and this news puts us in the best possible position to make it 30."
Virgin Trains has operated long distance services between London and Scotland on the West Coast line since 1997. It is owned by Virgin (51%) and Stagecoach (49%).
It has introduced a number of transformations on the railways such as tilting trains, automatic compensation for delays and a Netflix-style streaming entertainment system.
Mr McCall said: "We're thrilled about the prospect of continuing and improving this record of innovation with the UK's first long-distance high-speed network, as well as with our friends and communities along the West Coast."
Union leaders have previously condemned the fact that large parts of Britain's rail network is owned by German, Dutch, French, Belgian and Italian state-owned railways.
They claim around 70% of rail routes in this country are wholly or partly owned by foreign states, with profits from fares subsidising operations abroad.
SNCF has operated France's intercity TGV service since 1981 and has the largest fleet of high-speed trains in Europe.
It runs around 700 high-speed journeys each day in France and internationally - not including Thalys or Eurostar - at speeds of up to 200mph.
The company's high speed division recorded turnover of 7.5 billion euros (£6.4 billion) last year, of which more than a quarter was from international operations.