The Holy Roman Empire had nothing to do with the Roman Empire.Charlemagne was a Frankish (French) king who was crowned emperor by the pope because the pope wanted to have some control over him. For the next thousand years the relationship between the various popes and emperors (they were actually the Austrian and Spanish royal family) ranged from luke-warm to downright hostile.
In the 8th century, after the rise of Islam had weakened the Byzantine Empire and the Lombards had renewed their pressure in Italy, the popes finally sought support from the Frankish rulers of the West and received (754) from the Frankish king Pepin The Short the Italian territory later known as the Papal States. With the crowning (800) by Leo III of Charlemagne, first of the Carolingian emperors, the papacy also gained his protection.
By the late 9th century, however, the Carolingian empire had disintegrated, the imperial government in Italy was powerless, and the bishopric of Rome had fallen under the domination of the nobles. Once again the papacy sought aid from the north, and in 962, Pope John XII crowned the German king Otto I emperor. In this revived empire, soon called the Holy Roman Empire, the pope theoretically was the spiritual head, and the emperor the temporal head. The relationship between temporal and spiritual authority, however, was to be a continuing arena of contention. Initially, the emperors were dominant and the papacy stagnated. The emperors themselves, however, set the papacy on the road to recovery. In 1046, Emperor Henry III deposed three rival claimants to the papal office and proceeded to appoint, in turn, three successors. With the appointment in 1049 of Leo IX, the third of these, the movement of church reform, which had been gathering momentum in Burgundy and Lorraine, finally came to Rome. It found there in Leo and in a series of distinguished successors the type of unified central leadership it had previously lacked.
With the papacy taking the leadership in reform, the second great phase in the process of its rise to prominence began, one that extended from the mid 11th to the mid 13th century. It was distinguished, first, by Gregory VII's bold attack after 1075 on the traditional practices whereby the emperor had controlled appointments to the higher church offices, an attack that spawned the protracted civil and ecclesiastical strife in Germany and Italy known as the Investiture Controversy. It was distinguished, second, by Urban II's launching in 1095 of the Crusades, which, in an attempt to liberate the Holy Land from Muslim domination, marshaled under papal leadership the aggressive energies of the European nobility. Both these efforts, although ultimately unsuccessful, greatly enhanced papal prestige in the 12th and 13th centuries. Such powerful popes as Alexander III (r. 1159 - 81), Innocent III (r. 1198 - 1216), Gregory IX (r. 1227 - 41), and Innocent IV (r. 1243 - 54) wielded a primacy over the church that attempted to vindicate a jurisdictional supremacy over emperors and kings in temporal and spiritual affairs.
This last attempt proved to be abortive. If Innocent IV triumphed over Holy Roman Emperor Frederick II, a mere half - century later Boniface VIII (r. 1294 - 1303) fell victim to the hostility of the French king Philip IV. In 1309, Pope Clement V left Rome and took up residence in Avignon, the beginning of the so - called Babylonian Captivity (1309 - 78), during which all the popes were French, lived in Avignon, and were subject to French influence, until Gregory XI returned the papacy to Rome. During the 13th and 14th centuries, therefore, papal authority over the universal church was exercised increasingly at the sufferance of national rulers and local princes of Europe. This fact became dismally clear during the Great Schism of the West (1378 - 1418), when two, and later three, rival claimants disputed for the papal office, dividing the church into rival "obediences"; in their desperate attempts to win support, the claimants opened the way to the exploitation of ecclesiastical resources for dynastic and political ends.
http://mb-soft.com/believe/txc/papacy.htm
I commend you on your ability to cut and paste, but the fact still remains that the relationship between the papacy and the Holy Roman Empire was often quite violent (Google “Sack of Rome”).