TL; DR: NO!

First of all, the opening days were largely a series of confused skirmishes, along the Franco-German border and in Belgium. The real fighting didn't really begin till the second week of August, when there was fighting in northern Serbia, north-eastern Galicia, Belgium, Eastern France and East Prussia.

Infantry since the 1870s, NEVER, I repeat, NEVER marched into combat rank-and-file, 'arms locked', side-by-side; that would be suicidal, and incredibly irrational. Since the Franco-Prussian War of 1870, the dominant formation for infantry in Europe was the skirmisher line, a horizontal line of men about 10 feet apart, advancing forward with fire and movement. Fighting crouched or prone, using the nap of the earth and whatever cover was available, had been common among European light infantry, like the German Jagers and the French Voltigeurs, since the mid-1700s. Machine guns were held back, to protect the flanks, lay down suppression fire, or provide defensive fire. Artillery was deployed forward on the field, or just out of sight, firing shrapnel typically, but increasingly High-Explosive.

/u/zagreus9 mentions the First Day of the Somme below. An excellent illustration of the many myths of the war, but of the Somme in particular. Of the 80 battalions that went over the top that day, 53, over half, crawled into no mans' land before the barrage lifted, closing up as close to the German lines as possible, and rushing the parapet. 10 rushed the enemy lines from the parapet, and 12 advanced at the brisk pace advised by General Rawlinson, but most of these were behind a creeping barrage, and were highly successful.

On that day, the two corps south of the Albert-Bapaume road, XIII and XV Corps, reached all of their objectives. North of the road, British forest penetrated the enemy's lines around La Boiselle, the Schwaben Redoubt, and the Leipzig Salient; most of these forces were driven out with great loss or withdrew before nightfall. Elsewhere, as at Sere, the first wave suffered heavy losses, but some platoons/companies made it through to the second, and even the third positions.

Long story short, TOTAL, UTTER failure on the First Day, ie never even reached the parapet, was fairly uncommon. Machine guns did reap a brutal harvest, but the big killer was and always was, artillery. 77, 100/105, and 150mm artillery pieces fired into no-man's land, cutting the follow up waves off from the initial wave, killing and wounding scores, and sowing the kind of chaos the individual machine guns and rifleman could take advantage of.

Well we need to define what we mean by "rank and fire". Do you mean "Napoleonic" by this statement? Well even then it was not "rank and file" truly and even then was a very fluid form of war but I'm assuming that's what you meant.

What you're likely encountering is the idea that in the early period (especially '15) of the war men operated in something called close order and tended to operate on a company (~240) men level separated into platoons of ~60. Platoons would tend to stay relatively close together. Why? Well, especially for the Germans, their forces were comprised largely of new volunteers or reserves (ie: "weekend warriors") who were not very battle tested.

It's from this the mythology arises as the reasoning of close order being performed was the same reason closer order was performed in Napoleonic times; it allowed the officer to keep a reign on his men, make sure they're going the pace they need to go, don't wander off, and mutually support each other morally and literally with rifle fire. However it was not Napoleonic or "rank and file"; they were not marching in lockstep shoulder to shoulder in other words. They were just roughly within earshot of everyone else. Really the difference is not nearly as major as some would like to imagine; whereas in '17 and '18 a platoons frontage would go about 400 yards (ie: with 30 men a 'rank' and two ranks deep of ~25 yards distance, each man had ~15 yards of room on average) and in '14 the average frontage would be more like 100 or 200 yards; that is ~5 yards between every man, about 15 paces in either direction.