The star-forming main sequence (SFMS) is a tight relation observed between stellar masses and star formation rates (SFR) in a population of galaxies. This relation is observed at different redshifts, in various morphological, and environmental domains, and is key to understanding the underlying relations between a galaxy budget of cold gas and its stellar content. Euclid Quick Data Release 1 (Q1) gives us the opportunity to investigate this fundamental relation in galaxy formation and evolution. We complement the Euclid release with public IRAC observations of the Euclid Deep Fields, improving the quality of recovered photometric redshifts, stellar masses, and SFRs, as is shown both with simulations and a comparison with available spectroscopic redshifts. From Q1 data alone, we recover more than $\sim 30\,\mathrm{k}$ galaxies with $\log_{10} (M_\ast/M_\odot) > 11$, giving a precise constraint of the SFMS at the high-mass end. We investigated the SFMS, in a redshift interval between $0.2$ and $3.0$, comparing our results with the existing literature and fitting them with a parameterisation taking into account the presence of a bending of the relation at the high-mass end, depending on the bending mass, $M_0$. We find good agreement with previous results in terms of $M_0$ values, and an increasing trend for the relation scatter at higher stellar masses. We also investigate the distribution of physical (e.g. dust absorption, $A_V$, and formation age) and morphological properties (e.g., Sérsic index and radius) in the SFR--stellar mass plane, and their relation with the SFMS. These results highlight the potential of Euclid in studying the fundamental scaling relations that regulate galaxy formation and evolution in anticipation of the forthcoming Data Release 1.