Manchester City centre-back Laporte declared for La Roja last month after being granted Spanish citizenship, leading to him being included in their 24-man Euro 2020 squad.
Laporte represented France at youth level, including the Under-21s, but was never handed a senior cap despite being called up by Deschamps.
The 27-year-old has made a positive start to his Spain career by helping his side to three clean sheets in his first four caps, while also scoring in last week's 5-0 win over Slovakia.
Spain finished second in their Euro 2020 group and are on course to face France in the quarter-finals should the heavyweight nations see off Croatia and Switzerland respectively in the last 16.
Deschamps insisted ahead of the tournament he was only ever contacted once by Laporte to discuss an injury issue, but the player has refuted those suggestions.
"They called me six years ago. But in 2019? No, they didn't call me. While I don't want to go over this again, I had sent a message and didn't get a reply," he told The Guardian.
"I have it here. Maybe [Deschamps] changed number, got a new phone. Could be. I don't know, but I replied to the same number he'd called from before.
"I didn't get a reply then. Anyway, given everything that happened, nor did I think I was important enough to France to have to inform them of anything.
"My importance to them has been more a media issue than anything. I've always been very clear that I'm going to be with those that want me, not those that don't.
"I'm not saying France didn't want me, but I'm grateful to those that bet on me. Spain did and I'm trying to return that faith."
Laporte's passing accuracy of 96.64 is the third-highest of any player to have played more than 90 minutes at Euro 2020, behind Axel Witsel (96.91) and Dedryck Boyata (97.74).
The former Athletic Bilbao man's 86.33 successful passes per 90 minutes, meanwhile, has been bettered by just five others, including new team-mate Pau Torres (94.52), reflecting how quickly he has settled in with his adopted national team.
"Everyone has different feelings. I felt comfortable coming with Spain, fully identified," he said. "That's what made me change everything.
"Also, my family hasn't spent eight years in Spain like me.
"I'd been in contact with Spain for years because they've always wanted me. Luis Enrique called. I took the decision.
"It wasn't easy at all. My family still lives in France and from very young I played there with the national team.
"There were family chats, discussions, an exchange of opinions, the same doubts there would be if you had dual nationality I imagine."