The new trains are jointly financed by SNCF,
Transports de Martigny et Régions and the Valais canton?
No, the article you linked gives the answer:
3 trains are financed by TMR and 4 trains by région
Auvergne-Rhône-Alpes
The yearly costs including costs of rolling stock on Swiss territory
are cofinanced by the canton of Valais (37%) and the Confederation
(63%), as far as earnings are not sufficient.