Stephen and Patrice drank in "the bar MacMahon," named for the Irish Frenchman Patrice de Mac Mahon, perhaps the most illustrious descendant of the Wild Geese who left Ireland in the 17th and 18th centuries. He was Duke of Magenta, Marshall of France, and President of the Third Republic.
MacMahon's forebears descended from the Dalcassians, lost ancestral lands during Cromwell's depradations in the 1650s, and left Ireland in the 1690s after the Catholic lords' disastrous support for England's deposed Stuart king, James II. Groomed for a career as a military officer, Patrice rose through the ranks of the French army from the 1820s through the 1850s and achieved the rank of Marshall in 1859. As a conservative politician in the 1870s, he remained committed to the ancient French aristocratic order but positioned himself somewhat precariously as a figure who could rise above the struggle between monarchists and republicans. His term as the French president ended unhappily in 1879 with a Republican electoral triumph. He died in 1893.
The Avenue Mac-Mahon in the 17th arrondissement is one of the dozen major Parisian thoroughfares that converge on the Arc de Triomphe, and has been so named since 1875. I have not been able to learn anything about the "bar MacMahon" that Joyce knew.