The simple answer would be that French was heavily influenced by German, since Germanic peoples migrated, invaded and governed the region for much of its Roman and post-Roman history. While Germanic peoples also governed Spain and Italy for a time, their numbers with respect to the natives were extremely low, and for the large part they tried to merge with the local culture rather reshaping it, and anyway, natives recovered the control not so long after. Unlike in France, were the latinized natives and germanic peoples (namely the Franks) intermixed a way too much and finally created a new people. The legacy from this can easily be seen, as French has sightly over a third of its vocabulary with germanic roots. French also has Celtic roots: they lived and governed there for centuries before the Romans. English also directly influenced French, specially during the Hundred Years War.

Nothing like this happened at the same extent in Spain and Italy. Spain was conquered and governed by the Visigoths for a few centuries after the Roman collapse, but the Visigoths were few in numbers and actively tried to merge with the local culture, and even more so, they were fascinated by the remains of the Roman society, and tried their best to preserve it! So the impact in the language is minimal, but you can see their legacy in laws, architecture and some people's names.

Afterwards Spain was invaded by the Muslim Arabs and Berbers, which dominated most Central and Southern Spain for much of the 8th to the 12th centuries. They had far more numbers than the Visigoths, though they were still highly outnumbered by the locals, but at difference of them, they actively tried to reshape society, with impressive results as the Emirate of Cordova became the wealthiest and most advanced society in the world for much of its duration. This greatly affected Spanish, as many words comes from Arabic and Berber roots, like Almohada (Pillow), Almeja (Clam), Alcancia (Moneybox), Azar (Luck), Barrio (Neighboor), Chisme (Gossip) and so on. The Christian Reconquistas would put to halt to this influence and even reverse part from it during the Inquisición, despite from this, even to this day about the 8% of the vocabulary has arabic roots.

In Italy, by other hand, aside some small Germanic influence at the north of the peninsula and Arabic influence at the south, the language remained mostly intact from foreign influence, generally speaking foreign migrants were never common in the peninsula, and when they were, they often were other latinized people from France or Spain, or Greeks and so on.

Now, all Romance Language derive from Vulgar Latin, the version of Latin actual used by the people (Classical Latin was only used by the Elites). Aside the foreign influences already described, the rest of the languages directly derive from Latin, both in structure and vocabulary. About the 91% of Italian's vocabulary and 88% of Spanish vocabulary comes from Latin, so the words are the same, just ordered and spelled sightly different. Vulgar Latin never changed too much, for example as a Spanish native speaker I can understand almost as clear Vulgar Latin inscriptions as English people can understand Shakespare. As for why it never changed too much, part of it has to do with the Latino identity, and part of it has to do with the Church's and some Kingdoms/Republics attempts to preserve Latin or otherwise prevent more changes to Spanish and Italian, and part of it has to do with the literary tradition of only writing in Latin until the late 15th century, which is not really a long ago, and part of it has to do with the Renainssance, which was the search and revival for Roman and Greek cultures.

There were pressures to not change everywhere! It still changed, though, but at an impressively slow pace, so we can still partially understand each other. Also we've been culturally, religious, migrational, economical and geographically connected for much of the history as well, so we influence each other, reducing the differences from time at time.

Portuguese and Catalan are also about the same thing, they share almost the same history as Spain. Romanian is also very similar, but I don't know much about their history and they have relevant Greek and Slavic influences, though still far less than French has of Germanic. It must be said that we can also understand French to some extent, but the vocabulary differs constantly enough to make communication very difficult, yet not impossible.