The answer to your question is no.
Countries are considered on equal footing, they are sovereign. For one country's court to compel another country the compelling court would have to have jurisdiction. The only possible scenario by which a court of another sovereign can have jurisdiction over another sovereign is if that other sovereign consents to jurisdiction. This of course would not be in that country's interests and as such they would not consent.
Furthermore, if France and the USA could just sue each other in each other's courts to resolve disputes what would be the point of diplomacy? France no more wants the USA to be able to sue France in US courts, than the USA wants France to be able to sue the US in French courts.
These principles come from long ago established international law. There are only four scenarios by which a court can exercise jurisdiction over a party:
○ Property in state attached at the commencement of law suit
○ Resident of the state
○ Consent, by appearing in court
○ Physically present in the state and served personally with process
For further explanation see Pennoyer v. Neff.
Additionally, you have the issue of sovereign immunity. The United Nations Convention on Jurisdictional Immunities of States and Their Property details how, and why, State's cannot be sued by other states unless they have consented.
The International Court of Justice is the exclusive court for state v. state claims.