The general framework for international civil aviation is the Chicago Convention, made of the Convention and its annexes. Under the Convention, scheduled flights over a foreign territory requires a permission which can be given under related terms and conditions (art. 4).
In the US, foreign airlines operates in compliance with US laws (FAR part 129) and an individual agreement (OpSpecs) with the US administration.
This agreement can be used to enforce compliance, as stated at §12.3.1:
12.3.1 Suspension or Revocation of Operations Specifications (OpSpecs). The compliance and enforcement program provides a wide range of options for addressing noncompliance. In addition to referring apparent violations to foreign governments for appropriate handling, options include administrative action in the form of a warning notice or letter of correction, the suspension or revocation of OpSpecs, civil penalties, injunctions, and referrals for criminal prosecution.
This may take the form of referring apparent violations to foreign governments. As @ymb1 mentions in his answer, this is not very effective.
But there are other possibilities from fining the airline to suspending the authorization to do business on the US territory (suspension or revocation of OpSpecs).
For example, operating at San Diego (KSAN) is allowed in OpSpecs only after PIC get a special qualification for Rising terrain close to runway. Lufthansa, a major airline, operated off their OpSpecs, they were fined for non-compliance when PIC where caught regularly landing at San Diego:
FAA Proposes $6.4 million Civil Penalty Against Deutsche Lufthansa Airlines
Such action against an airline of any country is possible because:
- The Convention reaffirms the sovereignty of a State for its own airspace (art. 1), and
- The action is not discriminatory, it applies equally to airlines from any country (art. 44g).