Is it permissible to eat meats concerning which there is doubt regarding their lawfulness, or where it is highly probable that they are unlawful, given the existence of companies that produce both lawful (halal) and unlawful meats, the difficulty in ensuring their adherence to halal standards, and the lack of sufficient oversight over halal certificates in France?

The basic principle concerning slaughtered animals is prohibition. If there is doubt about the slaughterer or the method of slaughter, the default is that it is obligatory to abstain. The mere writing of "halal" is not sufficient if it is widespread that the slaughter is not in accordance with Islamic law. However, if the Muslims in charge of the mosques bear witness to the permissibility of the slaughtered animals, and their trustworthiness has not been disproven, then the default is that what they have testified to is permissible. But if their negligence in testifying is proven, then it is obligatory to advise them and compel them to ensure the fulfillment of the Shariah conditions before issuing a certificate of permissibility. If it is known that certificates are given to those who mix the unlawful with the lawful, then it is obligatory to abstain from all of them as a precaution against the unlawful.