I'd suspect that the world where the French invented the internet would be a very different one indeed, and it would be hardly impossible to see it being the dominant language there. In our universe though.... it is questionable.
The internet invention's period in the 1970s onwards is too late to make French into the world's global language at the present time, but it could easily be part of a TL where French is the primary political and cultural language in Europe. During the 1970s it was the lingua franca within the EEC, and you can see that in the way that acronyms and agreements came from the era - think of STABEX, ie. the Système de Stabilisation des Recettes d'Exportation (Export Earnings Stabilization System). It took decades until after the EU was established that English got the privilege of having an EU press conference done in the language, and it wasn't until the 2000s from my recollection that the percentage of documents originally written in English surpassed those written in French at the European Commission. It would be relatively easy to have a French internet and a few other accomplishments stave off decline and solidify French's position at the center of the EU politically, in a permanent manner.
Commercially, I have my doubts, since inherently commerce is more internationalized and internationally English is dominant, although it might be enough for an expanded role and for a much more multilingual tech center. After all, the effect is a snowball one: French can't hope to have the same dominance that English does, realistically, due to the difference in population size and world political influence. But a significant reduction in US influence and a higher French influence means that other languages have less incentive to learn a foreign language, which means decreased influence of the big languages and less incentive to learn them etc. etc.
The exception of course is technical terms, but even there there is a lively difference between what the Académie française specifies as being the word, and what is actually used. Case in point: wifi. The Académie française tried to get accès sans fil à Internet (ASFI) adopted, and it is the official recommendation.... but everybody calls it wifi. Things are always more flexible than what the rules say on paper, and the French are notorious for having a strong centralized state which they then proceed to ignore.
There's also nothing inherent in why this is so to French, despite the existence of the Académie since the 17th century. For a long time, the Académie française was very marginalized, during much of the 19th century when French was the indisputable world lingua franca. Instead the model was much more along the Anglo-Saxon model, where what constitutes words was more defined by dictionaries. The AF is something very useful for attempting to defend what French is in a world where there seems to be a threat from an outside language : if the situation is reversed, there isn't as much need. I'd suspect that rather than the predominance of the AF leading to the weakening of French, it is rather the weakening of French which has lead to the predominance of the AF.

Its also useful to look at the four leaders : Clemenceau is probably unique among French leaders in speaking good English since he lived in the US for a while. The Italian leader, Orlando, spoke French... by contrast, he didn't speak English, and the Anglophone leaders didn't speak French. Naturally it made it a bit difficult for him to communicate directly to the Anglo-Saxon leaders!
The internet invention's period in the 1970s onwards is too late to make French into the world's global language at the present time, but it could easily be part of a TL where French is the primary political and cultural language in Europe. During the 1970s it was the lingua franca within the EEC, and you can see that in the way that acronyms and agreements came from the era - think of STABEX, ie. the Système de Stabilisation des Recettes d'Exportation (Export Earnings Stabilization System). It took decades until after the EU was established that English got the privilege of having an EU press conference done in the language, and it wasn't until the 2000s from my recollection that the percentage of documents originally written in English surpassed those written in French at the European Commission. It would be relatively easy to have a French internet and a few other accomplishments stave off decline and solidify French's position at the center of the EU politically, in a permanent manner.
Commercially, I have my doubts, since inherently commerce is more internationalized and internationally English is dominant, although it might be enough for an expanded role and for a much more multilingual tech center. After all, the effect is a snowball one: French can't hope to have the same dominance that English does, realistically, due to the difference in population size and world political influence. But a significant reduction in US influence and a higher French influence means that other languages have less incentive to learn a foreign language, which means decreased influence of the big languages and less incentive to learn them etc. etc.
English was certainly the first among equals, but it was hardly dominant to the exclusion of other languages - in the Soviet Union for example, it assigned its foreign language learning as 50% English, 25% German, 20% French, and 5% Spanish, and English was only beginning to make serious inroads into the EU in the 1970s and 1980s.English was already the dominant Lingua Franca for decades before the Internet became a thing.
French has a formalized register of words which is more centralized, but English effectively accomplishes the same thing. Would you really use a newly adopted word into English in an official document or business agreement? The first result I got in google after looking up "most recent English words" is a good example. How many would you use in a formal context or setting? I'm guessing very few. Same in France, new words get created or adopted from other languages all the time, but they'll be used in informal speech. French has a centralized structure for dealing with terminology, English a decentralized one, but the effect is going to be the same for many affairs, and below the formal registrar, whatever official institutions say is largely meaningless.There are a lot of reasons that English tends to dominate International commerce, probably the biggest one is that English is so flexible with adoption of new words.
French is pretty much the mirror image of English, to the point that the French speaking nations actually meet on a semi-regular basis to come up with "proper" French terms for various words that have leaked into French (this is best seen in the very different terms used in tech, but is also done for other terms). This is both good and bad, since anyone who is fluent in French understands what the hell another French speaker is saying, provided the speakers are from countries that take part in the regular conventions (so American Cajun French dialect is quite different from Standard), but it also make the language far less flexible and can result in people having to effectively continually relearn terms.
The exception of course is technical terms, but even there there is a lively difference between what the Académie française specifies as being the word, and what is actually used. Case in point: wifi. The Académie française tried to get accès sans fil à Internet (ASFI) adopted, and it is the official recommendation.... but everybody calls it wifi. Things are always more flexible than what the rules say on paper, and the French are notorious for having a strong centralized state which they then proceed to ignore.
There's also nothing inherent in why this is so to French, despite the existence of the Académie since the 17th century. For a long time, the Académie française was very marginalized, during much of the 19th century when French was the indisputable world lingua franca. Instead the model was much more along the Anglo-Saxon model, where what constitutes words was more defined by dictionaries. The AF is something very useful for attempting to defend what French is in a world where there seems to be a threat from an outside language : if the situation is reversed, there isn't as much need. I'd suspect that rather than the predominance of the AF leading to the weakening of French, it is rather the weakening of French which has lead to the predominance of the AF.
The Treaty of Versailles is actually really amusing because of the two wikipedias on the matter. largely the French wikipedia is the same as the English one. The main additional section? One talking about the inclusion of English as being on equal footing as FrenchOr butterfly the First World War, America stays isolationist. IIRC the 'primary' language of the Treaty of Versailles was still French.
Its also useful to look at the four leaders : Clemenceau is probably unique among French leaders in speaking good English since he lived in the US for a while. The Italian leader, Orlando, spoke French... by contrast, he didn't speak English, and the Anglophone leaders didn't speak French. Naturally it made it a bit difficult for him to communicate directly to the Anglo-Saxon leaders!