I have to display a very long list of element in alphabetical order. I have thought of something like : http://csm-bcc8d3.webflow.io/alphabetique-index
Do you think it's a good idea to put the letters in a tab ?
Yes, Tabs with alphabet ranges can be a good option in this case. You might also want to consider a way for the user to get to a specific alphabet directly. As shown below, you can have a place user can type 'C' tab out and then you take the user to C entries directly or you could also have an auto complete field in its place where typing C would display all C entries right there as options (drop down choices display) and user can pick the entry. For browsing the lists, tabs will be useful. For taking the user straight to the entry if they already know what they are specifically looking for the text box/auto complete will be useful.
Could the list be organised hierarchically instead of alphabetically? Then you could use an accordion or a collapsible tree.
If using the alphabetic approach, I think tabs would be better, as it is analogous to a card index.