Hi again,
I've managed to display what I wanted ! The importation of data is really slow (it takes about 10 min to process the data for a week, which represents about 250k lines of data), but it works.
Here's how I did it, in case someone tries to do the same thing as I did :
let
Source = AzureStorage.Blobs("myazureblobsource"),
#"datastorage" = Source{[Name="datastorage"]}[Data],
#"Filtered Rows" = Table.SelectRows(#"atastorage", each [Date modified] > #datetime(2016, 4, 18, 12, 3, 22)),
#"Combined Binaries" = Binary.Combine(#"Filtered Rows"[Content]),
#"Combined Text" = Lines.FromBinary(#"Combined Binaries",1),
#"Json joined" = Replacer.ReplaceText(Lines.ToText(#"Combined Text"),"}{","}#(cr)#(lf){"),
#"Json Text" = Replacer.ReplaceText(#"Json joined","#(cr)#(lf){",",#(lf){"),
#"Json Text Complete" = Text.Combine({"[", #"Json Text", "]"}, ""),
#"Json list" = Json.Document(#"Json Text Complete"),
#"Data table" = Table.FromList(#"Json list", Splitter.SplitByNothing(), null, null, ExtraValues.Error),
Basically I had to transform the combined binaries into a list of Lines, then join the Lines into a Text (with Lines.ToText), then I replaced what I needed to be replaced in the text. Finally, I passed this text as an argument for Json.Document, split the result for it to be interpreted correctly by Power BI.
I did not include the last part of the process, which is the expansion of the JSON into a table, because the code was generated by Power BI when I clicked on the double arrows and it's really long.
Cheers 