Can France refuse to prosecute a case even after declining extradition?

Yes. While France is obliged to submit the case to its prosecuting authorities, French prosecutors retain discretionary power under the principle of opportunité des poursuites. They may decline to prosecute if evidence is insufficient, if the alleged conduct does not constitute a crime under French law (dual criminality requirement), or if the statute of limitations has expired under French law. The requesting state cannot compel prosecution. In practice, cases involving complex foreign evidence or weak documentation are frequently closed without charges, though this outcome depends heavily on the quality of the original criminal complaint.