French Emperor Napoleon III saw France as the protector of the Latin peoples, and had an ambitious plan to establish Mexico as a bulwark against the United States.

France invaded Mexico during the U.S. Civil War, which rendered the U.S. military unable to intervene.  Part of the French emperor's plan was a linkup with the Confederacy, thus neutralizing U.S. ability to thwart the French strategy.

On May 5th, 1862, north of the city of Puebla, the French Army under General Charles de Lorencez fought the Mexican army, under the command of General Ignacio Zaragoza. [....]

The Mexican army was on the hills, and the French had to fight uphill, never an enviable position to be in. Each army had the same quantity of cannon.

The French army tried and failed to assault the Mexican positions thrice, and by the third assault their cannon had run out of ammunition.  So French troops had to attack without artillery support.  After the third failure they retreated, harassed by Mexican cavalry, and then it started to rain.

So Mexico won the battle, and Zaragoza sent a one-line report to President Juarez: "The national arms have been covered with glory."  The young general died only 4 months later, succumbing in September of 1862 to typhoid fever.

The 1862 Battle of Puebla was not the end of the French Intervention, which continued until 1867.  As well, besides the determined opposition of the republican army of Benito Juarez, the French also faced U.S. pressure (the Civil War had ended), and the Prussian threat back in Europe.  So Napoleon III called it quits in Mexico and withdrew.

The 1862 Battle of Puebla had been a great morale booster for Mexico, and is still the most famous battle of the war, by far.

The Battle of Palo Alto. On May 8, 1846, United States and Mexican troops fought the first major battle of a two-year war on a broad expanse of salt-prairie called Palo Alto. As General Zachary Taylor's 2,300 U.S. soldiers marched to end the Mexican bombardment of Fort Texas, their outpost on the Rio Grande, General Mariano Arista's 3,400 men blocked the road, determined to maintain their siege. The ensuing cannon battle would last from midday to nightfall, ending without a true decision. However, the casualty figures-- 9 killed, 43 injured, on the U.S side and more than 125 wounded and 200 killed on the Mexican side--foretold the course that war would follow until its conclusion 16 months later with the American occupation of Mexico City.

The Palo Alto battle was but one of a series of intertwined clashes along the Rio Grande. When disputes about the ownership and boundaries of Texas had escalated into war, fighting first erupted with a skirmish at Rancho Carricitos. With war underway, Mexican forces had concentrated on eliminating the U.S. base, Fort Texas, constructed in disputed territory across the river from the city of Matamoros. The Palo Alto engagement and a decisive May 9, 1846, fight at Resaca de la Palma, were prompted by the siege of Fort Texas and resulted in a victory for U.S. forces. Following the U.S. occupation of Matamoros, on May 16, the region became a staging area for U.S. troops as combat plunged toward the heart of Mexico.

Though the battle of Palo Alto was a brief encounter, its impact was felt far beyond the field. The clash revealed the strength and innovation of American firepower, particularly of the quickly-positioned, rapidly-fired "flying" artillery that decimated Mexican lines. Success at Palo Alto and Resaca de la Palma showed the merits of a standing army and a military academy, in an era when Americans had questioned their worth. In time, dozens of young officers, including Ulysses S. Grant, James Longstreet, George Meade, and John Pemberton would use the battle and the war as a springboard to noted military careers. Following an overwhelming U.S. victory at Resaca de la Palma, the American population also rallied to support what had started as an unpopular, unwanted war. Likewise, General Zachary Taylor channeled his new-found repute to kick-off what would become a successful run for the Presidency.

For Mexico the impact was much less positive. The American fire power at Palo Alto surprised a Mexican force that had recently felt sure of its ability to stand up to the United States. The effects of the cannon barrage, seen in the piles of killed and maimed, demoralized the soldiers, helping to insure their defeat at Resaca de la Palma. The ultimate loss of the contest for the Rio Grande extended the depths of despair. Throughout the war, Mexican defenders never regained the confidence needed to fend off the U.S. advance. Nevertheless, many officers of the Mexican army who served at Palo Alto and other battles would move on to hold important military and political posts following the war. Most notably, General Mariano Arista, who lost his command following Resaca de la Palma, recovered his stature and became President of Mexico in the 1850s.