Hi! First things first:
Comment puis-je réduire mon accent anglophone autant que possible?
In case of subject-verb inversion like in your interrogative sentence, "peux-je" doesn't work: it always becomes "puis-je". This is only true for the first person singular form. "Can he?" would be "peut-il ?" for example.
Now about your recording: overall your accent is very easy to understand, and you sound like you speak French fluently. I can also hear that you are going for a French-Canadian accent. The fact that I can hear that is probably also good evidence that your pronunciation is already very good.
That being said, you do have a slight English-speaker accent. Here are some little mistakes or oddities I noticed:
When you said "laisser de côté", I heard "laisser des côtés". Make sure you don't pronounce the vowel in "de" as an "é".
The way you said "dessins" in "les dessins de serpents" was hard to understand because you pronounced the "in" part as an "i" followed by an "n". It should be a nasal vowel instead - I shouldn't be hearing any "n" sound. The way you said it sounded like "les dessines de serpents".
You pronounced the "T" in "serpents boas ouverts ou fermés". Since this is the masculine form, it should be silent. If you wanted to pronounce the laision between "ouverts" and "ou" (which is an optional liaison), you'd have to pronounce the "s" as a "z". The "T" would remain silent.
The way you combined the "g" and the "r" in "géographie" sounded a bit unnatural. Just practise on pronouncing both sounds clearly - in your recording they sort of sounded like one single exaggerated "R" sound.
When you said "à l'histoire", I heard "à l'hèstoire". Make sure you pronounce a full "i" sound there.
The way you said "calcul" was hard to understand because the "a" sort of sounded like an "è", and your "u" sound wasn't clear enough. It sounded sort of like a mix between an "u" sound and an "ou" sound.
The way you pronounced the "gr" in "grammaire" was a lot better than in "géographie". It sounded a bit like "crammaire", but at least it was clearly made up of two different sounds.
As the other commenter pointed out, when you said "abandonné", the final "é" sounded exactly like the "ay" in the English word "day" instead of sounding like a French "é".
The final "s" in "l'insuccès" should be silent.
Once again when you said "mon dessin numéro 1", I heard "mon dessine numéro un". You pronounced a perfect "in" sound in the word "peintre" earlier.
The way you pronounced the vowel "deux" in "mon dessin numéro deux" sounded too much like an "o" sound. Your tongue should be pushed more forward during the "eu" sound. To pronounce a perfect "eu" sound, round your lips as if you were going to say a French "o", then try to say "é" while keeping your lips in that rounded position. The resulting sound will be the "eu" in "deux".
Your "an" sound in "grandes" was different from the way you pronounced the "an" sound in "fatigant" and "enfants". It sounded like you said "les grindes personnes", but was perfect in "fatigant" and "enfants".