All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The basic ruling with regard to food is that it is permissible, not prohibited, and there is no difference between buying vegetables or fruits or other foods from a disbeliever or a Muslim. If you mean “meat” by Halal food, then if the store is for A Muslim, you should trust and believe him, and you are not required to investigate and verify it. As for the store owned by a Non-Muslim, if he says that he bought it from a Muslim or one of the people of the scripture (Christian or Jews), then you should believe him because this falls under the transactions section. It is a section in which the report of a Non-Muslim is accepted, even if he is not one of the people of the scripture. Durar Al-Hukam Sharh Gharar Al-Ahkam - from the books of the Hanafis - reads: "
"The report of the disbeliever is acceptable even if he was a Magian. If you bought the meat from a Muslim or one of the people of the scripture, it is Halal, but if you bought it from a Magian, it is Haram. It was stated in (Al-Kanz): The report of the disbeliever is acceptable in Halal and Haram matters (in transactions) … It was noted in (Al-Kafi): The report of the disbeliever is acceptable in Halal and Haram, to the extent that if he sent a Magian servant or a hired person to buy him meat, and he bought it and said I bought this from a Jew, a Christian, or a Muslim, then it is ok to eat such meat. Otherwise, it is not permissible. [End of quote - abridged]
But if he says that he is the one who slaughtered it according to the Sharee'ah, then it is necessary to ascertain whether he is one of the people of the scripture or not, because the slaughtering of a disbeliever other than the people of the scripture is not permissible. If it turned out that he is from the people of the scripture, then the basic rule is that the food of the People of the ٍScripture is permissible. However, if the common practice in that country is that they do not slaughter according to Sharee'ah, then the basic rule here is in contradiction with the common practice, and we have mentioned previously in our fatwas in the Arabic section that common practices shall have the priority over the basic rules in the countries where there is a lot of slaughter in a non-Islamic method, and the reports in this matter are too many to be assure and follow the basic rule. Therefore, one should be cautious as long there is doubt, so the probability of being slaughtered according to Sharee'ah is very weak, and this is enough to make you avoid it.
Allah knows best.