“C’est X qui …” has the same meaning as “X …”, but with emphasis on X. The way we French speakers perceive it is that “c’est X” is a statement of fact, which is always true. Françoise found the solution at a time in the past, so “… a trouvé la solution” is in a past tense. But the truth of that fact does not change over time.

There may be languages where a similar construction uses different tenses. That’s life. Languages often use tenses in different ways.

More precisely, “c’est … qui” is in the time of discourse. When you’re speaking now about present observations, the time of discourse is the present. In a narrative set in the past tense, the time of discourse would be the past, so one would write “c’était” (imparfait for an intemporal statement in the past). (Or say “c’était”, but spoken discourse is rarely in the past tense.) If the time of discourse is the future (which is unusual, but can happen), the correct form would be “ce sera”.

Here are a few examples to illustrate some of the possible cases.

— Le rendement a doublé ! Comment avez-vous résolu le problème ?
— Je ne sais pas. C’est Françoise qui a trouvé la solution, demandez-lui.
(— The yield doubled! How did you solve the problem? — I don’t know. Françoise is the one who found the solution, ask her.)

Ils parvinrent finalement à résoudre le problème en mars. C’était Françoise qui avait trouvé la solution.
(They finally managed to solve the problem in March. Françoise was the one to find the solution.)
[Note the different past tenses: “parvinrent” is a passé simple because it’s an event at a specific point in time. “Était” is an imparfait because it’s a fact that is continuously true, stated in the past. “Avait trouvé” is a plus-que-parfait because finding the solution happened in the past compared to the time of the discourse, which is the time the solution was applied.]

Je parie que c’est Françoise qui trouvera la solution. Elle est très compétente.
(I bet Françoise will be the one to find the solution. She’s highly competent.)
[“C’est” is in the present because I’m making this claim in the present.]

In cases where the stated fact is perceived at a time in the past or the future, “c’est” can either be in the present or at the time of perception.

J’ai bien vu que c’est Françoise qui a trouvé la solution. Je lui ai préparé une récompense.
J’ai bien vu que c’était Françoise qui avait trouvé la solution. Je lui ai préparé une récompense.
(I did see that it was Françoise who found the solution. I’ve arranged a reward for her.)

Vous verrez que c’est Françoise qui trouvera la solution. Elle est très compétente.
Vous verrez que ce sera Françoise qui trouvera la solution. Elle est très compétente.
(You’ll see that Françoise will be the one to find the solution. She’s highly competent.)

The results below are rough results; re-editions have not been taken into account.

(3) c’était lui qui a : 2 (This correspondence does not feel right, not natural.)
c’était elle qui a : 2
(2) c’est lui qui a : 49 (This correspondence and the following do feel right, natural.)
c’est elle qui a : 38
(4) c’est lui qui avait : 20
c’est elle qui avait : 14
(5) c’était lui qui avait : 33
c’était elle qui avait : 44

The pairs in the table, except one, express the same meaning, there is no nuance. In one of them (2,3) there seems to be an incompatibility, which seems to be the opposition between actions finished in the past (passé composé) and actions that have no definite end in the past (imparfait). Not all possible combinations have been stated and numerous impossible ones have not been mentioned; only the most common ones figure in the table. The following query and its main answer corroborate well the present answer: ref..

C’est Françoise qui a trouvé la solution.

C’était Françoise qui a trouvé la solution.

This is exactly like English, which is relevant as the OP speaks English and this compares the English and French. Knowing they are the same helps the OP to use the French correctly.

It’s Françoise who found a solution.

It was Françoise who found a solution.

C’est and C’était just like It’s and It was
are diectic references. For an explanation, please read the link below.

It’s Françoise who found a solution. The solution was found in the past but statement about Françoise is true in the present.

It was Françoise who found a solution. is merely a statement about the past.

deixis