Since the ban on single-use plastic articles in Europe, the food contact material (FCM) industry has been forced to move to more sustainable alternatives. Paper and board FCM are convenient alternatives but must be safe for consumers. This study aims to investigate potential migrations of various substances (e.g., plasticizers, photoinitiators, primary aromatic amines, mineral oil, and bisphenols) from straws and takeaway articles made of paper and board. Twenty straws and fifty-eight takeaway articles were carefully selected and investigated using liquid and gas chromatography coupled with tandem mass spectrometry or flame ionization detector. Fourteen substances of all the targeted categories were found in takeaway articles, including seven plasticizers, two photoinitiators, one primary aromatic amine, two bisphenols, and the saturated and aromatic fraction of mineral oil (MOSH and MOAH, respectively). In straws, fewer substances were detected, i.e., six substances, including three plasticizers, one photoinitiator, MOSH, and MOAH. At least one of the target substances was detected in 88% of the samples, demonstrating the importance of further evaluation of these materials. Finally, the associated risks were assessed, highlighting the potential risks for several types of articles regarding bisphenol A, one primary aromatic amine (3.3-DMB), and MOSH and MOAH.